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This problem comprehension or schema knowledge is facilitated when the schema underlying a given text is used as a vehicle to translate the information in the text into a semantic representation. this would involve restating the problem, identifying the problem type (i.e. change), discerning relevant and irrelevant information, determining information that is needed for solution, and representing the problem as a diagram (Mayer, 1999).  Problem solution requires representing the problem as a number sentence or list of operations or identifying subgoals for multistep problems (i.e. strategic knowledge) and carrying out single or chains of calculations (i.e. procedural knowledge; Mayer 1999). Because additive problem structures (i.e. change, group, compare) involve a "family" (e.g. 3, 5, 8), connecting the number family to the problem structures is critical to problem solution (Van de Walle, 2004). Although procedural knowledge is important, it (is extremely limited unless it is connected to a conceptual knowledge base" (Prawat, 1989, p. 10).  SBI- Schema-based instructionGSI- General strategy instruction SBI Components (some not necessarily all) a) SBI that used either number line diagrams to understand the semantic structure of compare word problems or schematic diagrams to solve a range of word problems. b) schema-induction instruction, c) SBI that explicitly taught for transfer by focusing on similar problem types, and d) SBI combined with metacognitive instruction.  different format, different question, unfamililiar vocabulary, irrelevent information, combining problem types, and mixing superficial features

Problem-based approaches to learning have a long history of advocating experience-based education. Psychological research and theory suggests that by having students learn through the experience of solving problems, they can learn both content and thinking strategies. Problem-based learning (PBL) is an instructional method in which students learn through facilitated problem solving. In PBL, student learning centers on a complex problem that does not have a single correct answer. Students work in ollaborative groups to identify what they need to learn in order to solve a problem. They engage in self-directed learning (SDL) and then apply their new knowledge to the problem and reflect on what they learned and the effectiveness of the strategies employed. The teacher acts to facilitate the learning process rather than to provide knowledge. The goals of PBL include helping students develop 1) flexible knowledge, 2) effective problem-solving skills, 3) SDL skills, 4) effective collaboration skills, and 5) intrinsic motivation. This article discusses the nature of learning in PBL and examines the empirical evidence supporting it. There is considerable research on the first 3 goals of PBL but little on the last 2. Moreover, minimal research has been conducted outside medical and gifted education. Understanding how these goals are achieved with less skilled learners is an important part of a research agenda for PBL. The evidence suggests that PBL is an instructional approach that offers the potential to help students develop flexible understanding and lifelong learning skills.

Problem Based Learning Academy is a well designed wiki with lots of interesting links/resources if you are interested in learning more about problem based learning. 

The website says: "THE Place For Educational Games!Our research-based and standards-aligned free educational math games and language arts games will engage, motivate, and help teach students. Click a button below to play our free multi-player and single-player games! In the future we'll add features enabling you to save records, tailor content for differentiated instruction, and pinpoint student problem areas." I think using the games in conjunction with a holistic approach to developing skills would make for a great way of getting students to practices some skills. Let students play, set goals, monitor those goals, reflect on their progress, and apply strategies/heuristics to specific problems they struggle with would create an environment in the classroom where learning was fun, self-monitored, and successful. 

Princeton scientist with an interdisciplinary bent has taken two well-known problems in mathematics and reformulated them as a physics question, offering new tools to solve challenges relevant to a host of subjects ranging from improving data compression to detecting gravitational waves.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here. On our website you will find thousands of our free mathematics enrichment materials (problems, articles and games) for teachers and learners from ages 5 to 19 years. All the resources are designed to develop subject knowledge, problem-solving and mathematical thinking skills. The website is updated with new material on the first day of every month. For guidance on how to find the right resources for you, go to the Help section of the site.

Interesting approach to using flip in a mathematics classroom. I love having students create product rather than just solving problems. I would even like to see students create their own problems in the future. 

"Stacey Roshan is using an approach dubbed by her students as the "backwards classroom."... The students watch pre-recorded lectures the night before the class, when homework problems are traditionally done, then spend the time in class getting answers to questions, working on additional problems with partners, and getting one-on-one assistance from the teacher. No more lectures in class." from The Backwards Class, by Dian Schaffhauser, THE Journal, 02/02/11

Contraption game, great for problem solving, logic, and fun! Doesn't address specific core content, but does offer students opportunity to explore, build, and persevere in problem solving situations. Great extra credit link. I think having students build models, share with the class, and make the goal to have lots of different examples to embed in a class wiki would be awesome!

Great examples of problems/data sets that can be analyzed. I do think there are a considerable amount of regression equations that may/may not be categorized appropriately. That said, it's a great set of questions to discuss with students, great data sets that can be updated with a little bit of research as most are 10 years old. One of the best compilations of regression problems that I've come across.

Reading is a Problem-Solving Process. Why Not Try the Thumb Method? New blog post by Denise Finley about supporting students while they learn to read scientifically!

Great article on looking at test preparation differently. It's not about answering a lot of questions similar to the ones on the test, but about learning processes that help students understand how to garner information from text/problems, etc. 

Welcome to the Physlets resource page. Physlets, Physics Applets, are small flexible Java applets designed for science education.  You do not need to become a Java expert in order to use Physlets.  The links on the right contain tutorials, download instructions, and example problems to help you use Physlets in your teaching.

While some professors seek to exclude the devices from the classroom, others are creating multimedia-rich curricula in which students can draw on online resources and interact with each other. Banning laptops is just plain wrong, according to Don Krug, associate professor at UBC's department of curriculum studies. He says students are adults, and the best a professor can hope for is a "respectful learning environment," where students limit their own behaviour. "If they really want to learn the information, they will. They're paying a lot of money," he says. "We're better off teaching them how to be responsible learners." Shows two polar solutions to laptop problems: total ban & adapting curricula to include multi-media interaction. Also presents respectful learning environment as best course for students who are adults. - comment by Kent Gerber

Easy tool to have students create connections between text and pictures. If the pictures from the site are used the issue of copyright won't be a problem. I like that it is incredibly easy to use.

Quantitative studies of school effects have generally supported the notion that the problems of U.S. education lie outside of the school. Yet such studies neglect the primary venue through which students learn, the classroom. The current study explores the link between classroom practices and student academic performance by applying multilevel modeling to the 1996 National Assessment of Educational Progress in mathematics. The study finds that the effects of classroom practices, when added to those of other teacher characteristics, are comparable in size to those of student background, suggesting that teachers can contribute as much to student learning as the students themselves.

Great site if you are looking for significant problems to let your students (higher level) ponder. Also, the organization of the site is impressive.

"In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples."