# PRESENTATIONS

On this page resides a selection of presentations I have given, listed in chronological order. All files (including the slides) are pdf format. Handouts are associated with some of the presentations.

The slides are best viewed with Adobe Acrobat in full screen mode. The slides were typeset with LaTeX and the Beamer package.

### Leonhard Euler:

**A (Very) Brief Look at His Life and Mathematics.**

This presentation was prepared in honor of Euler’s 300th birthday. A small selection of interesting mathematics that originated with Euler follows a short biography.

This was the keynote address at the first Walton Math Fest in April 2007. This presentation was repeated at the Georgia Mathematics Conference in October 2007.

### My Favorite Algebra Problems:

**A Personal Selection of Algebra Challenges for Student Enrichment or Math Teams**

This presentation showcases some excellent algebraic math team problems (and their solutions) taken from the State Mathematics Tournament, ARML practices, and the Rockdale Math Competition.

This was presented at the Georgia Mathematics Conference in October 2007.

### Calculus as Problem Solving

I believe that calculus should be taught from a problem-solving perspective. This short presentation demonstrates how to achieve that while still preparing students for the Advanced Placement exam.

This was presented at the October 2008 AP Content Workshop sponsored by the Georgia Department of Education.

### Opportunities for High School Math Teams:

**Contests and Tournaments at Your School and Around the Southeast**

After many talks over the years about “How to Run a Math Team,” this was the first talk prepared using LaTeX and Beamer, so this is included and the earlier presentations are not. This is a short summary of all the stuff available for a Math Team in Georgia.

This was presented at the October 2008 Georgia Mathematics Conference.

### Twelve-and-a-Half Days:

**An Adventure in Meta-Planning**

How does one plan effectively? It begins by planning for days that are unavailable for instruction: testing days, field trips, and other interruptions. Just how many days are there left to teach? Only 12 and one-half eight-hour days per class. This presentation outlines how I came to this conclusion, and offers some suggestions on what can be done about it.

This was presented at the October 2009 Georgia Mathematics Conference.

### Math Education in Georgia Reflected Through the State Math Tournament

Presented with Debbie Poss (Lassiter High School), this presentation examines the nature of the problems on the state math tournament and how that nature has changed over the past three decades. From rote bookwork-type problems to high-level thinking, the state tournament serves as a reflection of the knowledge we want students to have and to use. Many example problems are included.

This was presented at the October 2009 Georgia Mathematics Conference.

### History of Mathematics:

**A Course for High Schools**

This presentation is an updated version of the original 2005 NCSSSMST talk about the year-long History of Math course. This was presented again at the 2007 Georgia Mathematics Conference. Now that the course is a semester-long GPS course, a this updated presentation was created. This describes the course goals and gives an overview of the curriculum.

This was presented at the March 2010 National Consortium of Specialized Secondary Schools for Math, Science, and Technology (NCSSSMST) Professional Conference.

### Typesetting Beautiful Mathematics with LaTeX

This presentation serves as an introduction to LaTeX -- what it is for, how it is used, and what the advantages are.

This was presented at the October 2008 AP Content Workshop sponsored by the Georgia Department of Education.

This was presented at the October 2010 Georgia Mathematics Conference and again at the November 2010 NCSSSMST Professional Conference.

A slightly updated version of this presentation was given again at the October 2015 Georgia Mathematics Conference.

### Energizing Your High School Math Team:

**Free and Low-Cost Opportunities for Math Teams**

With school districts cutting back and budgets being slashed, I felt it was prudent to tweak my usual Math Team presentation for GMC a bit. This presentation focuses on the free opportunities for Math Teams and discusses some ways to raise funds. Suggestions are given for what to buy with those funds as well.

This was presented at the October 2010 Georgia Mathematics Conference.

### Mathematics Enrichment Through Math Teams (the Georgia Way)

Aimed at an audience either new to Math Team or an audience from outside Georgia, this talk is an introduction to Math Teams from the perspective of an enrichment activity. Example problems illustrating requisite problem-solving skill and advantages to starting and maintaining a Math Team are included.

This was presented in November 2010 at the combined National Association for Gifted Children Annual Convention and the NCSSSMST Professional Conference.

### Discrete Calculus:

**(Most of) Calculus Through Euler’s Method**

This presents my technique of introducing calculus to students in terms of “rate equations.” Euler’s Method is the fundamental tool of this approach, and it is used extensively. It is even used to derive a discrete version of the Fundamental Theorem of Calculus.

This was presented twice on behalf of the Georgia Department of Education’s AP Regional Workshops: October 3, 2011 in Perry, Georgia and October 7, 2011 in Dalton, Georgia.

### Problem Solving Strategies for Math Teams (Or, How to Count)

Aimed at an audience of Math Team sponsors who are looking to widen their own or their students’ breadth of knowledge, this talk is an introduction to combinatorics and counting strategies.

This was presented at the October 2008 AP Content Workshop sponsored by the Georgia Department of Education.

This was presented at the October 2011 Georgia Mathematics Conference.

### Exploring the Use of Graphing Calculators on Math Competitions

I was secondary speaker behind the lead speaker, Charlie Koppelman at Kennesaw State University. This presentation reviewed results from a statistical survey sent to schools that participate in the KSU Math Contest, and then provided examples of math contest problems in which the graphing calculator plays various roles.

This was presented at the October 2012 Georgia Mathematics Conference. (There are no slides posted because Charlie wrote them, not me!)

### Georgia ARML: We Have a State Math Team?

I was secondary speaker behind the lead speaker, Tom Fulton from iLearn, Inc. We educated the audience about all things Georgia ARML, from selecting the team to coaching the team to the tournament itself.

This was presented at the October 2012 Georgia Mathematics Conference. (There are no slides posted because Tom wrote them, not me!)

### Teaching Integration

I used to teach integration in a traditional way with a focus on symbolic manipulation in the quest to find antiderivatives. This presentation focuses on how my teaching of integration has changed over the years of teaching calculus. Now I focus more on the meaning of definite integrals, on accumulation functions, and the application of the Fundamental Theorem.

This presentation was done on behalf of the Georgia Department of Education for the AP Regional Workshop at Bradwell Institute in Hinesville on November 9, 2012.

### The Gambler, the Stutterer, and the Cubic:

**An Historical Account of the Solution of the Cubic**

As the title suggests, this is a presentation of an interesting episode in the history of mathematics. This concerns the 16th century controversy surrounding Cardano (the gambler) and Tartgalia (the stutterer) and the credit for being the first to solve the general cubic equation.

This presentation was conducted as part of the Walton High School Math Fest in Marietta on March 30, 2013.

### Teaching Integration

This is a different version of the presentation above.

This presentation was done on behalf of the Georgia Department of Education for the AP Regional Workshop at Bainbridge High School on October 9, 2013 and again at Rockdale Career Academy on October 11, 2013.

### An Approach to Teaching Infinite Series

I used to teach infinite series in a traditional way with nary a mention of series until the end of the year. I have changed my ways by introducing sequences, some series, and Taylor polynomials at certain points in the year before teaching infinite series. I also talked about how useful the Root Test for Convergence is (even though it is not part of the AP Course Description).

This presentation was done on behalf of the Georgia Department of Education for the AP Regional Workshop at Rockdale Career Academy on October 11, 2013.

### Making Your Math Team Successful

Aimed at an audience of Math Team sponsors who are wondering what to do with their Math Teams, I answered such questions as “What should practices be like?”, “What things should my Math Team do?”, “How do I get students to problem-solve?”, and “What can I do to keep interest alive?”

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This was presented at the October 2013 Georgia Mathematics Conference.

### Solving Calculus Problems: A Hands-On Session

I was secondary speaker behind the lead speaker, Marshall Ransom at Georgia Southern University. This session gave calculus teachers a chance to explore calculus concepts related to the AP exam by giving them carefully constructed problems. The problems were written by Marshall and me. There are no slides, since there was not a formal presentation. However, the problems and solutions are posted.

This was presented at the October 2013 Georgia Mathematics Conference.

### Slope Fields, Differential Equations... and Maybe Euler’s Method, Too

This presentation offers an alternate approach to teaching slope fields and Euler’s method -- normally taught at the end of the course in conjunction with differential equations -- earlier in the course, as an application of derivatives.

This presentation was done on behalf of the Georgia Department of Education for the AP Regional Workshop at Rockdale Career Academy on October 10, 2014.

### Taylor Series, Maclaurin Series, and the Lagrange Form of the Remainder

This presentation offers an approach to introducing Taylor polynomials earlier in the year, as an application of derivatives.

This presentation was done on behalf of the Georgia Department of Education for the AP Regional Workshop at Rockdale Career Academy on October 10, 2014.

### So You’ve Decided to Start a Math Team... What’s the Next Step?

Aimed at an audience of Math Team sponsors who are wondering what to do with their newly-formed Math Teams, I answered such questions as “How should I get students to join?, “What things should I advertise Math Team?”, “How do I get everything paid for?”, and “What contests and tournaments should we do?”.

This was presented at the October 2014 Georgia Mathematics Conference.

### Georgia’s State-Wide Math Team (Or, All About ARML)

What is Georgia ARML? This presentation attempts to answer that question and others, such as: How are students selected for the Georgia ARML team? What happens at Georgia ARML practice? How can teachers get their students prepared for ARML?

This was presented at the October 2015 Georgia Mathematics Conference.

### Implementing Changes in the AP Calculus BC Curriculum

This presentation outlines the new developments in the AP Calculus BC course, taking effect in the 2016-2017 school year. I also offer some suggestions on implementing these changes.

This was presented at the October 2015 Georgia Mathematics Conference and again on behalf of the Georgia Department of Education for the AP Regional Workshop at Lambert High School on October 23, 2015.

### Table Problems in Calculus

Here is a collection of calculus problems involving functions defined by tables. All aspects of calculus are presented through the lens of table problems: limits, derivatives, definite integrals, differential equations, the Mean Value Theorem, and more.

This was presented on behalf of the Georgia Department of Education for the AP Regional Workshop at Lambert High School on October 23, 2015.

### Mathematical Problem Solving with Math Teams

One aspect of problem solving is often overlooked: similarity between seemingly unrelated problems. This is where the presentation starts, and combinatorics, algebra, and number theory problems follow which illustrate how knowing a method is more important than knowing a formula.

This was presented at the October 2016 Georgia Mathematics Conference.

### Scoring Free-Response Questions

The presentation describes how to score Free-Response Questions through a case study of one particular AP Calculus Free-Response Question: AB/BC4 from 2018.

This was presented at the October 2019 Georgia Mathematics Conference.

### Teaching Advanced Finite Mathematics

The presentation describes the curriculum of the Georgia Department of Education's fourth-year math option, Advanced Finite Mathematics. I wrote the standards and learning objectives for this course, and this is my presentation on the course.

This was presented at the October 2023 Georgia Mathematics Conference.

### Teaching History of Mathematics

The presentation describes the curriculum of the Georgia Department of Education's fourth-year math option, History of Mathematics. I wrote the standards and learning objectives for this course, and this is my presentation on the course.

This was presented at the October 2023 Georgia Mathematics Conference.

QUESTIONS?

If you have questions or comments,

feel free to contact me by emailing cgarner (at) gctm (dot) org.