## Solutions to math problems are explained step-by-step.

One of the most difficult concepts for the K-12 student in the mathematics classroom is translating a mathematical solution into words. This may be the result of the level of abstraction needed to make the transition from a numerical solution to the written word. Another potential stumbling block for students when writing solutions to math problems is that students often have a tendency to solve the problem and then immediately jump into writing the solution without ever preparing for the writing process. Finally, writing across the math curriculum has never been incorporated effectively because a method of transcribing mathematical processes has never been clearly defined for either instructors or students.

Not every book has answers in the back but these days it’s pretty easy to check your answers anyway. Most graphic calculators can handle very complex scenarios, and give you a check (provided you have solved step one; make sure you know the problem). The Internet also contains a myriad of solutions to math problems from the basic to the complex. That said, sometimes the solution is the best wrong solution! Advanced math problems often require you to take these same steps and come to the right wrong answer; a true test of your mathematics solving skills!

* on how to write solutions to math problems

* CMU (peer tutoring and academic counseling resources)

* and more illustrating calculus concepts

* at CMU

**Joanne Lobato**received a three year grant from the National Science Foundation,

*Re-imagining Video-Based Online Learning.*

The familiar YouTube-style videos of solutions to math problems have been used world-wide to help students learn basic math. Dr. Lobato’s $440 thousand grant will allow her team to create and test a model of online videos that embodies a more expansive vision of both the nature of the content and the pedagogical approach than is currently represented in YouTube-style lessons. Rather than the procedurally-oriented expository approach of videos that dominate the internet, the videos produced for this project will focus on developing mathematical meanings and conceptual understanding. They will feature pairs of middle school and high school students, highlighting their dialogue, explanations, and alternative conceptions. Despite the tremendous growth in the availability of mathematics videos online, little research has investigated student learning from them. Consequently, a major contribution of this proposed work will be a set of four vicarious learning studies. The grant provides funds a research assistantship for C. David Walters (on right in photo), a student in the Mathematics and Science Education Doctoral Program (MSED) For arguments sake, we shall say we need a heuristic anytime we solve a problem that is non-numeric. The reasoning is that such problems usually require human intervention, and all human actions/behaviors/thoughts are infinite by nature. Take the example of bending a finger. One is tempted to say this involves only the pulling of the finger toward the palm. In reality, to bend a finger the brain first generates the idea to bend the finger. Once the idea establishes itself in the brain, then signals are sent to all of the muscles involved to either contract or relax at a specific moment in time. But, the brain signal alone contains a series of steps where neural transmitters are secreted and the neurons are turned either on or off. The all-or-nothing quality of neurons themselves involves even more molecular process. Eventually, we find ourselves at the atomic level, then the quantum level, until, before we know it, we are playing with the very essence of infinityspace-time. But, we still havent defined how the initial thought of bending the finger was generatedto do such would guarantee us the Nobel Prize. Anyway, somewhere along the line we have to make a decision of when we can say that we have provided enough information to solve the problem. Hence, we make a generalization and, by definition, we have created a heuristic. An algorithm is any step-by-step solution. Since math education is concerned with deriving rigorously exact and accurate solutions, then the solutions to mathematical problems are, by their very nature, finite. Thus, we can solve any math problem with a finite number of steps and in doing so we establish a need for the algorithm. Instant solutions to math problems: look over the various links on the home page until you find a topic that seems to describe the math problem you're working on. Select a link then another and you will be presented with a blank form into which you can type your math problem for Webmath to solve.