(Part 2) Best products from r/matheducation

As a first step, you should decide what your dream career is. You're considering a Master's degree - why not a PhD? Or maybe a second Bachelor's in a related field would be more appropriate? It all depends what you want to do as a career.

You might want to see this book: https://amzn.com/0521797071 - This book won't teach you everything, but it could help you get started. Then start looking into the math GRE (the math subject test - not the math part of the general GRE). Buy some prep books for that and try taking a practice GRE. See how much of that material you know.

Once you attempt a practice GRE , it should help you figure out how prepared or underprepared you are. At this point, you will probably want to sign up for some senior-level undergraduate math classes like Calc 3, Real Analysis, and ODEs. Once you can get an acceptable score on the GRE, you should apply to graduate programs.

If you're able to, I think you should consider a PhD program with a teaching assistantship. These programs offer a tuition waiver and a small stipend as payment for you teaching. Master's students often don't get any financial support. It's possible to complete a PhD program without getting into debt, and picking up a Master's along the way is optional.

Keep in mind that a graduate program might require you to take some undergraduate courses. If they don't require it, they might suggest it. You should take their advice and sign up for these classes. I had to take undergrad Real Analysis during my first semester as a graduate student, and everything worked out fine.

Good luck!

When you say everyday calculations I'm assuming you're talking about arithmetic, and if that's the case you're probably just better off using you're phone if it's too complex to do in you're head, though you may be interested in this book by Arthur Benjamin.

I'm majoring in math and electrical engineering so the math classes I take do help with my "everyday" calculations, but have never really helped me with anything non-technical. That said, the more math you know the more you can find it just about everywhere. I mean, you don't have to work at NASA to see the technical results of math, speech recognition applications like Siri or Ok Google on you're phone are insanely complex and far from a "solved" problem.

Definitely a ton of math in the medical field. MRIs and CT scanners use a lot of physics in combination with computational algorithms to create images, both of which require some pretty high level math. There's actually an example in one of my probability books that shows how important statistics can be in testing patients. It turns out that even if a test has a really high accuracy, if the condition is extremely rare there is a very high probability that a positive result for the test is a false positive. The book states that ~80% of doctors who were presented this question answered incorrectly.

Not much of theory to base your teaching on, but A mathematician's lament is a nice read.

I like Papert, so you could read Mindstorms or look about Constructionism (his theory).

There are some French guys that I like as well, such as Brousseau and Duval. Duval in particular is very nice.

As for general pedagogy, you could read on the classical psychologists, such as Piaget and Vygotsky, or an introduction in general to see which ideas you like best.

A lot of the advice I have comes from "Best Practices" which our math team members share. That way, our kids go from 6th grade to 7th to 8th with some similar structures and procedures in place.

As for not getting into a rhythm, you could have a vaguely bullet-pointed Agenda at the front. I do this daily; it looks like this:

Agenda

• Attendance, Announcements, Questions
  
  
• Review HW (workbook)
  
  
• Distributive Property (notebook)
  
  
• Worksheet (Partners/Groups)
  
  Even if the Agenda is a little off, kids have an idea where they stand, and you have a roadmap of your class activities, even if you don't tell them how much time you expect each activity to take.
  
  If your homework review is taking too long, cut out the stuff which is painfully long or otherwise feels unproductive. I found myself going over every problem, which was downright boring to some kids. What works for me is to have students check answers with each other while I walk around with a grade book or my tablet to see who completed the assignment (for my class, I give them 5 minutes tops, and they start the moment they sit down). This is a time which must not become "off-task" time for some kids -- setting this routine early in the year really helped. They learn to ask each other questions, and compare answers, and do some basic peer-mentoring/review. Then I say something like "Okay, even if you're not finished, we're going to go over the answers, so get settled." I have a projector and an iPevo document camera for the next step: I put the teacher's edition under the camera and display the answers on the board, and read them out loud quickly, not asking if they want to go over them until the end. For each different section/concept on the page, I say "does anyone need me to any of problems nine through fourteen? No?...Okay, what about fifteen through eighteen?" Remind them they'll see this on the quiz, or on a standardized test (which makes it "them vs. the problem", or "them vs. the standardized testing board", rather than "them vs. you"). Repeatedly doing HW problems which cover the same concept is a time waster. Usually one problem per section is plenty -- any more, and they can take notes, read their book, or come to extra help.
  
  If you feel like your homework check is going too long, you can also set expectations for your students; tell them up front that you'll only be spending 10 or 12 minutes going over the homework, and stick (pretty close) to it. Cover the problems you feel most important, if you have a choice. If you don't have a document camera/projector combo, I found numbering the problems and answers on the board without doing all of them was an acceptable compromise.
  
  I never grade homework for right/wrong -- the sheer volume and time it would take (to collect, to organize, to grade, to hand back...) is too impractical. Besides, I'm not so organized as I would need to be to do it. Our kids have a workbook which really doubles as their textbook. The way I keep them honest is with a weekly quiz. I tell them which pages and which days of material it will cover, so they know what to study in their notes. Instead, I don't collect the homework; I grade their homework on how complete it is -- did they do all the problems? Did they show their work in places they would need? My department head suggests letting kids do work in their heads, but only if they can demonstrate their ability to get right answers that way. I find it takes time for me to get to know the kids before I can tell who really is able to do it in their heads, and whether any student is simply making their homework look completed for credit.
  
  I hope you find some worth in my suggestions; I realize we all teach very differently, and my methods might not fit your style at all. Best of luck with it. Let me know what works for you, if anything!
  
  -onwardknave
  
  edit: formatting bulleted list
  
  

The Parrot's Theorem is a light, quick read. Follows the history of mathematics in a murder mystery sort of way. Not Earth shattering, but fun.
Also The Mathematician's Lament by Lockhart. Really does a great job of exploring what mathematics is at heart, and what the focus of math education should be (i.e. learning to appreciate the beauty in number and pattern, etc.)

There are some great tips and resources here. Teaching math is definitely an uphill battle, also within yourself. It shows you deeply care about your students and do not wish to subject them to the form of institutionalized child abuse that most math classes are.

I cannot give you a silver bullet. This is a journey you have to take on yourself, and there are no shortcuts. But what I can point you to are the best teachers I have learned from. Dan Meyer's 3-Act Math is a great start, as mentioned by others. I can also wholeheartedly recommend James Tanton (www.jamestanton.com, www.gdaymath.com). His content is also the basis for a lecture series "The Power of Mathematical Visualization" on The Great Courses and for the globalmathproject.org.

A lot of great teachers are also on Twitter (best professional decision I have ever made): Jo Boaler, Ed Southall, Sunil Singh, just to name a few. They each have also written wise books, more than I can name here.

But I will mention Out of the Labyrinth. It was a real eye-opener on how to teach math through puzzles and playful problem-solving. Who doesn't love puzzles? A great puzzle doesn't look like math as you tackle it, yet when you look back, you will see that you have learned a great deal of math, just without the obfuscating jargon. Paul Zeitz has written a great book about it (although with more advanced topics than you probably need in your class).

In general, learn about the Eastern-European schools of mathematics, esp. the Russian and Hungarian ones. They rely heavily on problem-solving instead of French-style stock-loading of unmotivated theory.

Finally, I have heard great things about the way math is taught in Japan, at least in lower grades. Translated textbooks are scarce, but their style is so visual and pictorial that you can get a lot of ideas from the illustrations alone. This connects back to using visualizations to supplement or even supplant calculations, as mentioned above.

Best of luck!

First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.

Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:

Geometry and solutions

Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.

A First Course in Calculus

For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.

Some more very good books that should be used more, by Gelfand:

The Method of Coordinates

Functions and Graphs

Algebra

Trigonometry

Lines and Curves: A Practical Geometry Handbook

I think it can be reinforced this way, but I feel that a lot of the asking of "why?" can be important for students, albeit annoying at times for teachers, and that may not come up in the same way with games(Though it also might).

Beyond this, there are students who do desire to continue with mathematics after the basic high school curriculum, and many of them do not really know that until after they complete some higher-level math courses like Calculus. So the math is still important.

That being said, I love bringing games in to the classroom. Though I typically stay away from anything advertised as a "math game." Instead, I bring games that I like, but in which mathematical concepts can be found. Some examples I've used in class include: Set, Mao, The Great Dalmuti, Settlers of Catan, and Formula D.

Honestly, if you're wanting an understanding of statistics, I'd recommend Statistics for Dummies. Don't be deceived by the title, you'll still have to do some real thinking on your own to grasp the ideas discussed. You might consider using textbooks or other online resources as secondary supports to your study.

I can also give you a basic breakdown of the topics you'd want to develop an understanding of in beginning to study statistics.

Descriptive Statistics

Descriptive statistics is all about just describing your sample. Major ideas in being able to describe the sample are measures of center (e.g., mean, median, mode), measures of variation (e.g., standard deviation, variance, range, interquartile range), and distributions (e.g., uniform, bell-curve/normally distributed, skewed left/right).

Inferential Statistics

There is a TON of stuff related to this. However, I would first recommend beginning with making sure you have some basic understanding of probability (e.g., events, independence, mutual exclusivity) and then study sampling distributions. Because anything you make an inference about will depending upon the measures in your sample, you need to have a sense of what kinds of samples are possible (and most likely) when you gather data to form one. One of the most fundamental ideas of inferential statistics is based upon these ideas, The Central Limit Theorem. You'll want to make sure you understand what it means before progressing to making inferences.

With that background, you'll be ready to start studying different inferences (e.g., independent/dependent sample t-tests). Again, there are a lot of different kinds of inference tests out there, but I think the most important thing to emphasize with them is the importance of their assumptions. Various technologies will do all of the number crunching for you, but you have to be the one to determine if you're violating any assumptions of the test, as well as interpret what the results mean.

As a whole, I would encourage you to focus on understanding the big ideas. There is a lot of computation involved with statistics, but thanks to modern technology, you don't have to get bogged down in it. As a whole, keep pushing towards understanding the ideas and not getting bogged down in the fine-grained details and processes first, and it will help you develop a firm grasp of much of the statistics out there.

The first place I'd look would probably be a physical book - something like this. Encyclopedia-style books with one concept per two-page spread would also be among my go-tos, but those might not be long enough for your purposes. Additionally, do you know anyone who did a history of mathematics class in university? Some of those classes are open to history majors as well as math majors, so they could potentially have more history than math.


Oh, and just for fun: here's a Christmas-themed piece about Pascal's Triangle.


I wish I had something more concrete to offer you. Best of luck!

> popular if controversial amongst math educators

I see some great suggestions being put forward on this thread. I am partial to CGI, which has a very strong research base, but this is technically a program for teachers learning to teach elementary math, not a curriculum for children. However, it is an easy read and gives great insights into how children learn arithmetic and how teachers can guide such learning.

Just a side note: teaching for conceptual understanding (which you seem to understand the importance of) is well accepted and not controversial at all among math educators, only among the general public and a few mathematicians, who sometimes do not understand the importance of a conceptual base in elementary education.

Do you know of similar guides or lists? Please contribute resources or books in a list here.

Remember, this is for teachers that also intend to become middle school teachers, and for this, a mathematics major is not necessary (there are many educated professionals changing their career to teach), so reconsider if you think this list is missing such advanced materials that a teacher may never even need mention in a classroom, let alone master. I'm not suggesting such advanced topics are inappropriate, but don't forget the audience, new teachers preparing for a successful beginning and beyond!

I'll begin:

Basic Mathematics:

• Precalculus by Sheldon Axler
  
  Calculus
  
  
• Calculus by Gilbert Strang. The book, the solutions manual, the instructor's manual, and a study guide are free to download from the author.
  
  
• Basic Calculus: From Archimedes to Newton to its Role in Science
  
  Mathematics Education
  (not your own, but as the subject)
  
  
• MATH! Encounters with High School Students
  
  
• On the Shoulders of Giants – New Approaches to Numeracy
  
  
• What's Math Got to Do with It?
  
  
• Math Made Visual
  
  
• Proofs Without Words and Volume II
  
  Education
  
  
• Nonviolent Communication
  
  
• Fires in the Bathroom, there is also a version for middle school but I haven't read it.
  
  Abstract Algebra
  
  
• Classical Algebra I'm still reading this, but it may be more appropriate for non-mathematics majors to understand that connection between the apparent chasm of school algebra and "modern" algebra.
  
  Number Theory
  
  
• The Higher Arithmetic This too may be more appropriate for someone not intending to master number theory.
  
  Mathematics History
  
  
• Men of Mathematics though I know there are better or more accurate histories, such as the one on the list by Morris Kline, but this one really is written well, though it doesn't have much mathematics, as it's more about the mathematicians.