Background and Goals

It is clear from report after report (CITES) that many students continue to fail to become interested enough in mathematics previous to, or during, middle school to acquire a good basic working knowledge of this important subject. The consequences for higher education or employment that can support a family are widely publicized.

A growing need, and where some of the most lucrative opportunities will increasingly exist, is in computer technology—ICT. Yet, college enrollments in this major have recently <declined> despite the promise of high incomes for graduates. As with mathematics, interest in computer programming—"coding"—will need to be stimulated early and continuously through high school to increase interest. There are not many ways to interest children and youth in writing computer code, but there is one that most students find attractive—the Logo computer language. Logo is the key component of the constructivist tool set that makes up the delivery vehicle of The Expert Mathematician instructional system. Students' attraction to dynamic mathematical learning can enable teachers to start strong and hold interest high throughout grading periods. In our training, they will personally experience how students can become exhilerated almost from the beginning.

Goals and objectives of onsite training:

1. Engage students—whether or not they've been previously successful in math—in an affectively positive and successful experience with mathematics at this crucial transitional time prior to high school.
• fill in gaps in concepts and skills
• gain confidence in mathematical problem solving
2. Improve students' critical thinking, problem solving and team collaboration skills.
• specific skills will be introduced with research evidence showing positive outcomes and workplace expectations.
3. Provide an engaging and sound introduction to computer programming with mathematical technology as experts use it in real work.

The third goal also helps meet a number of educational technology standards for students and teachers as suggested by ISTE, 2007, 2008. Teachers will see these goals come to life in our hands-on instructional format.

How is TEM innovative?

There is a cluster of social, psychological and cultural factors that influence how much effort students will invest in any subject. Certain conditions "turn on" the intent to learn—what psychologists call volition. To the degree volition is sufficiently activated in students, just about any student can learn just about anything offered, or required, in the standard k-12 curriculum.  Therefore, the most important task of an instructional design is to turn on, or turn up, volition to the level needed for success. This is especially crucial in mathematics, which requires careful thinking over long periods to master the basics through algebra. <National> and <international> test scores repeatedly remind us of how difficult it is to activate volition in mathematics. The Expert Mathematician instructional system is a truly innovative entry that builds on the interests of the technology generation, holding the promise to bring up volition to learn math.

Teachers who are trained in constructivist technology applications or have instincts for helping students "internalize" their learning experience will feel immediately at ease with The Expert Mathematician. Teachers whose main experience is more in line with direct instruction, but who have found motivating students to do the work very difficult, will see a substantial difference when those same students "internalize" their math learning experience in TEM's approach.

Hands-on; On-site

Teachers often report that staff training taken off-site is difficult to implement back in the classroom. We overcome this disconnect via a two part training that ends in a middle school classroom with actual students. This can be done in one day. Teachers will have sample instructional materials, the dynamic learning software and a tutorial that introduces the software prior to the training day, so you will be generally familiar with the mechanics of the program prior to taking part in on-site training. We request that you also introduce students to the functionality of the software, so training can focus mainly on classroom pedagogy. The Logo computer software works the same on both PC and Apple brand computers.

Morning Training Session

The morning session is conducted in a computer lab of your choosing, ideally at a middle school in your district. We introduce teachers to some relevant basic theories related to the power of social learning, the importance of teaching students how to productively communicate while collaborating on problem solutions together—and, how teachers can more easily activate deep, investigative thinking in the middle school math classroom using The Expert Mathematician program. The power of multi-sensory, multi-dimensional, collaborative learning will be emphasized. This basic introduction is mostly hands-on. Teachers will work together in pairs at a computer station, as their students will—while our instructors model (and discuss) the roles teachers will assume back in the classroom.

During this introductory session, teachers will discover how TEM's intuitively smooth, custom design can lead students into an "internalizing" experience. What we call the "generative learning advantage" is inherent in the combined design of our copyrighted and trademarked learning materials and our version of the Logo dynamic mathematics software. This combination engages students in real mathematics, like experts doing real work use math to "make things." It is an empowering and compelling experience—even for most students who have not previously shown interest in learning math.

Afternoon Training Session

Recommended: After a lunch break, we will work in a classroom with middle school students. A block schedule running about 90 minutes permits more indepth instruction, though standard 50 minute classes can work, but due to introductory discussion, training time with students on computer activities will be limited. Only classrooms where Internet access is not available during training sessions must be used.

Trainers will place a few instructional posters in your classroom that help establish students' expectations about how the dynamic peer learning environment works and briefly discuss the challenges and opportunities of working in this way—as well as employers' expectations (also on a poster) that students will have these skills.

We will then run a "live" experiential classroom, modeling for teachers how to start students "down the runway" and ease them into an "internalizing" learning experience.

Many questions that come up during the morning session will be answered as we work with students during the afternoon session. Follow-up email support will also be available.

Trainers can also be available for multiple sessions, as needed.

Volition and "Internalization"

These two intentional processes drive learning and work reciprocally. As they build and reinforce one another, learning deepens. As this process develops, TEM naturally evolves a learning community. As the learning community develops, teachers are encouraged to add further internalization interventions. For example, TEM provides rubrics. Suggestions are also included in instructional guidelines for prompting students to write up key mathematical points of their lessons on the computer's output screen. Digital projectors can be used for student presentations. Students can save their work as live, editable Logo files or in jpg format for emailing to peers. This feature creates opportunities for distance collaboration that can cross oceans with a key click. These features create a robust experience for many youth that can pave the way to higher level studies in computer technology, as well as mathematics, and development of skills that serve state and national STEM goals.

How high teachers take students' internalizing experience will depend somewhat on their own mathematical creativity, but use of a dynamic mathematics language tends to build that, too.