# Instructors

## The goal of Mathable

Mathable presents a complete rethinking of:

- Mathematics as an empirical science.

- How to present mathematical ideas visually.

- How students can make the transition from mathematics in the classroom to mathematics outside the classroom.

- What motivates students to do mathematics.

- Helping students realize that mathematics is a discipline connected with reality.

- How to give students a sense of accomplishment.

- How to motivate students to want to write about mathematics.

- Best practices on using technology in mathematics education.

Unlike any other mathematics course, Mathable attempts to actively involve students in their own learning by putting them in a position to acquire mathematical ideas visually. This means that instead of hanging technology on the end of the learning process, Mathable uses technology to initiate the learning process. It accomplishes this through its electronic interactive text, as described above, and it invites students to write about the mathematics they are doing as they are doing it. Typically, Mathable students learn by doing in the lab and attend no lectures.

## Structure of the courseware

The National Research Council report, Moving Beyond Myths, describes Mathable’s calculus courseware as follows:

“An innovative calculus course [which] uses the full symbolic, numeric, graphic, and text capabilities of a powerful computer algebra system. Significantly, there is no textbook for this course-only a sequence of electronic notebooks.

Each notebook begins with basic problems introducing the new ideas, followed by tutorial problems on techniques and applications. Both problem sets have “electronically active” solutions to support student learning. The notebook closes with a section called “Give It a Try,” where no solutions are given. Students use both the built-in word processor and the graphic and calculating software to build their own notebooks to solve these problems, which are submitted electronically for comments and grading.

Notebooks have the versatility to allow re-working of examples with different numbers and functions, to provide for the insertion of commentary to explain concepts, to incorporate graphs, and plots as desired by students, and to launch routines that extend the complexity of the problem. The instructional focus is on the computer laboratory and the electronic notebook, with less than one hour per week spent in the classroom. Students spend more time than in a traditional course and arrive at a better understanding, since they have the freedom to investigate, rethink, redo and adapt. Moreover, creating course notebooks strengthens students’ sense of accomplishment.”

This is a good description, but it does not mention the Literacy Sheet component of each lesson. Each lesson in the courseware consists of four parts:

• *Basics* – a Mathematica Notebook with problems with full discussion and answers.

• *Tutorials* – another Mathematica Notebook with more problems with answers.

• *Try It* – Mathematica Notebook with more problems whereby students utilize the full power of Mathematica (graphics, symbolics, numeric and written response) to arrive at their own solutions to problems.

• *Literacy Sheet* – printed problems in the printed supplements waiting for hand written responses.

Students use the *Basics* and the *Tutorials* as research materials for solving *Try It* problems in much the same way as research mathematicians use journal articles as research materials.

The *Literacy Sheets* are used after the student has completed the Give It a Try assignment to hone students’ skills away from the computer.

Mathable’s Calculus courseware series (formerly Calculus&Mathematica) was written within the guidelines of the NCTM Standards and National Research Council reports “Everybody Counts” and “Moving Beyond Myths.”

## Grading

Everyone dreams of a calculus course that teaches itself and requires no grading. Mathable almost teaches itself. Class preparation time is negligible. So where’s the catch? You guessed it; the catch is the grading! If you are going to have a successful course, then you’re going to have to do a lot of it. The heart of Mathable is student work on the Try It problems. These problems are best assigned either one or two at a time. It is important to grade assignments promptly so that students receive feedback and can correct any misconceptions. Many successful instructors create a formative dialog with students, allowing students to revisit the problems that are not completely correct for another try. You will find that as you grade your student’s work, you will learn what they understand, what they are struggling with and can then follow up with a classroom discussion that will engage student interest.