Summer, 2017

- Ph.D 1994 in Mathematics - Ohio State
- Professor at UNC-Asheville since 1997
- Third year working with FCR-STEM

- Fractals and chaos
- Computational tools to
- Aide the research process
- Illustrate mathematics at all levels

- Teaching

- To teach you some math!

- As a participant in a professional development program, you're here to improve your teaching of mathematics.
- I'm told that many of the CGI techniques you're learning have been in practice for some time.
- Research shows they work.

- Research on CGI is ongoing.
- One new question: how does teacher content knowledge impact student learning?
- Much of the math we see will be applicable in your classroom fairly directly.
- Direct applicability is not necessarily the main objective, though.

I happen to be the happy father of a proud 8 year old.

- Practical arithmetic
- with Algebra!

$26+4=?$

\begin{align}
26+4 &= \color{blue}{(20+6)}+4 \\
&= 20+\color{blue}{(6+4)} \\
&= 20+10=30
\end{align}

Looks like we used the

$$(a+b)+c = a+(b+c)$$

$$(1+2)+3 = 1+(2+3)$$

$$(20+6)+4 = 20+(6+4)$$

We also used

If $a=b$, then $P(a)=P(b)$

$26=20+6$, so $26+4=(20+6)+4$.

(20+6) + 4 = 20 + (6+4)

Slip

$26+17=?$

Flip

Looks like we threw in the

$$a+b = b+a$$

$$2+3 = 3+2$$

$(2x+6)+(x+7)=?$

Note how similar this is to the last question.

In fact, if $x=10$, this is the last question.

- Substitution
- Associativity
- Commutativity
- Distributivity
- Arithmetic using these

- How the rules arise from direct modeling
- Using the rules to do arithmetic
- Standard algorithms

- Uses of the equals sign
- Algebra

- Geometric/symbolic feedback
- Place value
- Something fun