Here are some sources that I find useful. Most are free.
These descriptions of the Common Core Math Standards by grade level are meant for parents, but would be helpful to anyone looking for a one-page overview plus an example for each grade.
How People Learn: Brain, Mind, Experience, and School, a publication of the National Academy Press. You can download free PDF files of the entire book here (or order the paperback for $24.95).
Adding it Up: Helping Children Learn Mathematics is another NAP publication, available for free (or not) here. A 52-page summary of Adding it Up, called simply Helping Children learn Mathematics, is also available; I used it in my first-year seminar (Mathematics for All).
Another NAP publication, How Students Learn: Mathematics in the Classroom, includes applications of the principles outlined in How People Learn to specific lessons in elementary mathematics.
The Common Core Standards website includes background information, Key Points, and “Myths vs. Facts” (worth a look), as well as links to download the entire document.
You might find it easier to take in the organization of the Common Core math standards by going to the Illustrative Mathematics site. This site also has a growing collection of tasks aligned with specific items in the Standards.
The Institute for Mathematics and Education at the University of Arizona has links to drafts of Progressions, “narrative documents describing the progression of a topic across a number of grade levels.” The first document, Draft Front Matter, is a good place to start.
Another site to support adoption of the CCSSM (and the English/Language Arts standards as well) is Achieve the Core.
For specific attention to the Standards for Mathematical Practice (SMP), see this site from the Educational Development Center. There is a comprehensive set of tasks for each of the eight SMP. There is also a student dialogue to go with each task. Note these instructions: “Before reading the dialogue, work on the mathematics task. Next reflect on the mathematical practices you engaged in while working on the task. Finally read the student dialogue.” Good advice.
The Mathematics Teaching Community website is a place to engage in detailed discussion. It’s also fun just to explore other people’s conversations.
The Inside Mathematics website is “a professional resource for educators passionate about improving students’ mathematics learning and performance.” There’s a lot here. I find the videos to be interesting and illuminating, but if I were a school principal or math coach I’d go straight for the “Problems of the Month” on the “Tools for Educators” page.
The National Numeracy Network website has teaching resources, columns, and descriptions of some interesting curriculum projects (mostly at the college level). The NNN also produces an open-access peer-reviewed journal, Numeracy: Advancing Education in Quantitative Literacy, available here.
I also used selections from Mathematics and Democracy in my first-year seminar. “The Case for Quantitative Literacy” provoked some interesting discussions.
I’ve now read the second edition of Knowing and Teaching Elementary Mathematics, by Liping Ma, which has some interesting reflections on responses to the first edition. I highly recommend this book. It’s not always a comfortable read, especially for U.S. educators, but there’s lots of food for thought about how we prepare teachers and support — or fail to — their own learning as they continue to teach.
When I first started looking into research on mathematics education, I had a hard time making my way through the jargon (i.e., standard vocabulary in a research area not my own?) in much of the literature. In contrast, the writings of Deborah Ball, a former classroom teacher, and her coauthors are refreshingly accessible. I participated in a workshop where she was a co-leader, and she’s just as cogent and insightful in person. She and Hyman Bass have modeled what collaboration between math education experts and research mathematicians can be at its best. Their (and others’) work on mathematical knowledge for teaching (MKT) is a good place to start; for example, this article (with Heather Hill).
Some of the videos from the 1999 TIMSS (Third International Mathematics and Science Study) are available online. You no longer have to register in order to watch the videos. There is a transcript for each video, as well as some class materials and commentary under the “Resources” tab. The comments are helpful for putting these lessons into cultural context.
While we’re on the subject of international comparisons, you can see all of the TIMSS results here, including the 2011 results (see link in the left column).
The National Council of Teachers of Mathematics (NCTM) is a membership organization, but parts of its website are available to everyone. Parents of young math students might find the “Family Resources” page helpful.