Table of Contents

Personal Reflections and Teaching Goals

Four of the courses I’ve taught are freshman level required classes for non-scientific related majors. Most students in those classes seem to have a very negative uninterested attitude towards mathematics and just want to get over with the requirement as soon and as painless as possible and then forget about it for good. In each of those classes I’ve tried to convey the importance, appeal and beauty of mathematics to the students. Unfortunately, some of the students’ comments after the course are that they can tell about my knowledge and passion for the field but they still dislike it deeply. I would love to find new techniques and alternatives to help the students brush away their bad feelings about mathematics and be able to see it, if not as a beautiful discipline, at least as a helpful tool.

When I taught M CC135 Patterns of Phenomena, a course designed for liberal arts majors, I really enjoyed the idea of presenting mathematics from a more philosophical, artistic and creative perspective. I would really like to develop a similar course and design specific materials that would make it very experimental.

On the other hand, I would also really like to teach higher level courses and have the opportunity to design research projects embedded in the class setting. In particular, I would like to develop a computer algebra system based linear algebra or abstract algebra course.

Finally, I plan on continuing my pedagogical education by accessing the faculty resources available on campus and attending specific mathematics education workshops and conferences.

Lesson Study Research Project

During the Fall 2002, Spring 2003 and Summer 2003 semesters I was a member of the Lesson Study: Creating Laboratories for Curricular and Instructional Enhancement research project at Colorado State University. The project included a three-hour weekly lesson study group (facilitated by the mathematics educator, the calculus coordinator, and graduate student instructors) which served as a laboratory for the development, testing, refining, and evaluation of lessons. During these sessions ten lessons were designed to improve the understanding of key calculus concepts. The lessons were then tried by the participating graduate students in their M CC160 Calculus for Physical Scientists I classes, with other members of the project observing and sometime videotaping the session. The Lesson Study group would then debrief the lesson and revise it based on the group comments.

Our two main goals were to develop intuitive thinking in the students through promoting questioning in general, favoring conceptual type questions, and incorporating cooperative learning activities. In January 2003 we all participated in an intensive week-end workshop on Cooperative Learning in Mathematics, led by Dr. Neil Davidson, Professor Emeritus and Senior Scholar of the University of Maryland., President: Mid-Atlantic Association for Cooperation in Education (MAACIE).

Professional Development Workshops

As part of the Certificate of Accomplishment in Teaching program at North Carolina State University I have attended several workshops about different aspects related to teaching and learning in the university classroom. Attending those lectures has really broaden my perspective on the tools one can incorporate in the classroom setting and has also awaken my curiosity about alternative methods I could appeal to when planning my lectures.

Included in this section are my reflections on a few of those workshops:
Engaging Students Series: Using Games in the Classroom.
Games in the Classroom, Part 2: Applying Bloom’s Taxonomy to Game Design.
Considering Student Expectations of Course Websites: A focus on content, media usage, and structure.
Did you teach your dog, Spot, How to Whistle? Learning Styles Examined.

Engaging Students Series: Using Games in the Classroom.

Part I: Description

Lead Presenter: Dr. Barbi Honeycutt

Assistant Director

Faculty Center for Teaching and Learning

North Carolina State University

Date of the event: October, 17th, 2006.

Location of the event: Faculty Center for Teaching and Learning conference room.

This interactive workshop aimed at showing some examples of games that can be used in the classroom as well as analyzing the techniques, benefits and challenges of game playing as a teaching tool.

There were ten participants at the workshop. After briefly introducing the topic and the agenda Dr. Honeycutt made us all play the Synergy Game. The game is played as follows: first participants scan through a fifty word grid for sixty seconds, and then they try to write down as many words as they remember. After comparing the number of words the participants could recall groups are formed to combine their word lists and determine the number of words each group obtained. This game helps the students understand the benefits of working in a group.

After playing the game and analyzing it we studied the benefits, challenges and considerations when including games as a teaching tool.

Then we all participated in the Bingo Memory Game. In this game the participants start by drawing a grid (we played with a 3x3) which will be the bingo card. Then the game leader posts some questions on the board/overhead (in this case there were 11 questions). Each player picks as many questions as spaces on the bingo card and answers each of them on one space of the grid. Once every player has filled out his/her card the game leader picks the questions in a random order (out of a box for example) and the players mark the corresponding spaces on their cards (we used Hershey kisses as markers) until someone has completed a row (vertical, horizontal or diagonal). If that person has the correct answers on his/her card he wins the game. This game helps the students assess their knowledge of a specific topic.

After debriefing the Bingo Game the workshop ended with a discussion about how to design games, which games to use for different classes and some advice on how to start including games in the classroom.

Part II: Analysis

I have incorporated games in my classes in the past, but most times I did it as a way to select students to go up to the board and answer a problem: I would for example bring Trivial Pursuit cards, pick a student at random and if they couldn’t answer the question correctly (they got to choose the category) they would have to go up to the board and solve one of the homework problems. I never really thought about using/designing games, as part of my teaching, to actually include class material or train the student’s skills.

I learned through this workshop that there is a distinct difference between playing games as a distraction and using games as a teaching tool. In the second instance, by incorporating a debriefing/analysis portion after playing a game designed with a specific learning objective in mind, the teacher can help the students reflect on their learning and assess their skills or knowledge on a topic.

I also learned that it is possible to find games that could be pedagogic in any area (although it might be harder in some!). I particularly enjoyed the Bingo Game because it would definitely be applicable in a Mathematics class, it was fun to play and it really helped the players assess their knowledge on a topic without putting them in a stressful evaluation environment.

I’ve always tried to incorporate experiential education methods in my classes because it really helps the rhythm (keeping it less monotone), student interaction and energy of a class and I cannot believe I never used games before. I am now looking forward to reading some of the references suggested by Dr. Honeycutt and designing some fun, dynamic AND pedagogic games to use in my future classes.

Games in the Classroom, Part 2: Applying Bloom’s Taxonomy to Game Design.

Part I: Description

Lead Presenter: Dr. Barbi Honeycutt

Assistant Director

Faculty Center for Teaching and Learning

North Carolina State University

Date of the event: March, 15th, 2007.

Location of the event: Faculty Center for Teaching and Learning conference room.

This workshop was the continuation of the “Engaging Students Series: Using Games in the Classroom” workshop, which Dr. Honeycutt presented in the Fall 2006. The workshop presented Bloom’s Taxonomy and discussed how to incorporate it into games that can be played in a classroom setting.

There were 6 participants at the workshop. After quickly reviewing the definition and main characteristics of games, Dr. Honeycutt presented Bloom’s Taxonomy. This categorization of the degrees of competence involved in the learning process includes six levels: knowledge, comprehension, application, analysis, synthesis and evaluation. In order to illustrate the application of Bloom’s Taxonomy to game design, we proceeded to play a game.

The game was called Wolfpack 101. Its goal was to assess how much the participants knew about North Carolina State University. The game was modeled after the well known television game show Jeopardy. After splitting up into three two-person teams and determining the turn order using a die, we took turns answering questions from six different categories: Famous Wolfpackers, History, Current Events, Campus Geography, Colleges & Departments and Miscellaneous. Each category had five different levels of questions. For each right answer, and depending on the level of the question, a certain number of coins, each worth $25,000, were awarded. At the end of the game the team with the most coins won a prize. The game applied Bloom’s Taxonomy by relating each question level with the corresponding level in the taxonomy.

After finishing the game we debriefed it. The consensus was that the game successfully fulfils its objectives by being fun to play, engaging the students in both cooperation (within the teams) and competition (with the other teams) and involving all the levels of knowledge and learning. The use of Power Point with hyperlinks to the answers made the game seem very close to the game on TV, which makes it exciting to play.

Before closing the presentation, Dr. Honeycutt talked about some of the goals and challenges in applying Bloom’s Taxonomy to game design as well as examples of games that can be played related to the different levels of the taxonomy.

Part II: Analysis

I really enjoyed this workshop a lot. I wasn’t familiar with Bloom’s Taxonomy, so it was very interesting to me to learn about this specific classification of the levels of knowledge and understanding of a topic or problem. I specifically liked the lists of cue words associated to each level of the taxonomy and how simple it is to use them in classifying questions. It was also very interesting to reflect on which levels of education involve which levels of the taxonomy and how doing research implies using Analysis, Synthesis and Evaluation, which are not necessarily used outside of this setting.

I have to say that I felt a little bit envious of the humanities and social sciences, for which I could think of multiple games applying Bloom’s Taxonomy to incorporate in a class setting, including even course-long games involving projects. I unfortunately have a hard time imagining something like that in a lower level Mathematics class.

Most of the basic Mathematics classes involve mainly the three first levels: Knowledge, Comprehension and Application. The next levels up are only present in higher level classes and active research, where as of right now I have a hard time envisioning incorporating games.

However, I think it would still be possible to use the tools and game ideas presented in this workshop in a Mathematics class, by restricting perhaps the Taxonomy levels present in the game. I definitely think the Jeopardy game would be a helpful tool to use, setting, for example, the first level questions to recall definitions and theorems, the next level for solving simple application problems, the following one for more theoretical examples or conceptual questions and the last level to analyze graphs, compare logic statements or find errors in proofs or statements. I definitely plan on implementing this game next time I teach a class.

I am definitely very interested in the development of games as a classroom tool for Mathematics and will continue to think about this topic in the coming months and whenever I teach a new class.

Considering Student Expectations of Course Websites: A focus on content, media usage, and structure.

Part I: Description

Lead Presenter: Dr. Traci Temple

Assistant Director for Instructional Development

Faculty Center for Teaching and Learning

North Carolina State University

Date of the event: October, 31st, 2006.

Location of the event: Faculty Center for Teaching and Learning conference room.

This workshop presented an overview of the media options that could be included in a course’s website as well as a survey of the expectations, needs and preferences that the current generation of college students have for the media content in course websites.

There were four participants at the workshop. After briefly introducing herself and talking about her background, Dr. Temple started the session by passing around a series of books related to web design and media, understanding the “internet” culture, and how teaching methods today should take into account the extensive exposure the students have  to television, internet, video games…

Afterwards Dr. Temple began her presentation by explaining the characteristics of the majority of the current college student audience: the “Net Generation” (born 1965-1980) and the “Millennials” (born 1981-1994) and how to incorporate constructivist influenced teaching/learning tools into web-based instruction.

Then Dr. Temple talked about what she learned about course website expectations and preferences from students she interviewed as part of her research and the conclusions she reached in her study about which features should be included and which would be detrimental to the student’s learning.

Throughout the presentation every point was illustrated by accessing a specific website and analyzing its features.

Part II: Analysis

At the beginning of the session Dr. Temple asked the participants whether they had (or had in past taught courses) a website. I mentioned I did but didn’t really elaborate. I thought my course websites were in general very basic and didn’t really “count”. However, after learning about Dr. Temple’s study results on students’ expectations I realized I didn’t do so badly: every item on the list was included in my website!

Of course, after looking at some of the examples presented I realized the vast amount of available options and how advanced some of the presented sites were. It seemed to me that in order to have well designed course websites as a professor one would need to either have available funds to hire a designer or spend an incredible amount of time learning website design and such, neither of which seems viable.  After bringing that point up for discussion I was reassured. First we all agreed that in certain areas, and in my personal case in mathematics, the overall design of the website can be fairly simple and still fulfill the student’s needs and expectations. Dr. Temple also talked about how students prefer their course websites to be rather plain and straight to the point. They expect them to look serious and professional and would in fact find it extremely annoying if they had to wait for flash applications, movies, animations, fancy graphics, and etcetera, to load.

After the presentation concluded we all had a very interesting discussion about what the right amount of technology and computer generated or accessible information should be. We all agreed that although it is convenient for the professor to present his/her lectures in Power Point (or similar), since it for easy posting on the course’s website, this brings multiple problems. By not writing down the information on the board professors tend to go through the topics rather fast, which gives the students no chance of processing the information or taking additional notes to detail the content of the “slides”. On the other hand, even if given enough time in between ideas it seems that students assume that if they are given lecture notes or slides they don’t need to supplement them and therefore assume a completely passive role during the lectures. I think this is and will always be a debatable topic, but our discussion was extremely interesting.

Did you teach your dog, Spot, How to Whistle? Learning Styles Examined.

Part I: Description

Lead Presenter: Dr. Alton Banks

Director

Faculty Center for Teaching and Learning

North Carolina State University

Date of the event: February, 22nd, 2007.

Location of the event: Faculty Center for Teaching and Learning conference room

This workshop presented the importance of knowing about the different styles for gathering, processing, and retaining information, or learning styles, and how to address them in a classroom setting.

There were 19 participants at the workshop. Dr. Banks’ talk started with a short presentation, based on the book “The Biology of Learning”, of the relationship between our brain, and more specifically the information transfer between the different areas of our brain, and learning. The teaching-learning dynamics were then explained, emphasizing the importance on the teacher adapting his/her teaching style to the learning audience in order to facilitate the learning process for all the students.

Before proceeding to explain the different learning styles, we were asked to answer a questionnaire, consisting of four sets of eleven questions, in order to determine our own learning styles, according to the Felder-Silverman Model. Dr. Banks then gathered the results in order to determine the group’s learning demographics. In our group, the majority turned out to be: active, sensor, visual, sequential.

After discussing our group results, we compared them to the results of different NCSU Faculty groups. Those in the quantitative areas tended to be: reflective, intuitive, visual, sequential. Those in the qualitative areas were active, equally sensor and intuitive, visual, global. Finally, those in the health related fields were reflective, sensor, visual, sequential.

Dr. Banks then proceeded to briefly present three different taxonomies for learning styles: Myers-Briggs, Kolb’s and Silverman-Felder and gave detailed descriptions of the categories in the Silverman-Felder model since it is the one we used in determining our learning styles.

The last section of the workshop addressed the question of how to adapt the teacher’s teaching style to the students’ learning styles. Most students are sensors, visual, sequential. However, it is possible to “teach around the cycle” by including items in the whole spectrum of the learning styles, which allows the teacher to facilitate learning for the whole audience, no matter their learning style, while encouraging them to expand their learning in styles other than their own.

Dr. Banks concluded his presentation by providing strategies and tips to appeal to all learning styles when teaching.

Part II: Analysis

This workshop was extremely interesting and engaging. I had heard about learning styles but didn’t really know how extensive the taxonomy is and how wide the range is. I was particularly surprised to assess my learning style, which turned out to be “balanced” (or “neutral”) between active and reflective, sensor and intuitor and sequential and global. I also had a moderate preference for visual versus verbal. If asked before answering the questionnaire I would have said definitely reflective, intuitor, sequential, verbal. Though surprised at the results I couldn’t help feeling a bit proud of being balanced in the first three categories, since I think it reflects my affinity between mathematics and music/dance/yoga.

On the other hand, before revealing which faculty group the statistics shown in each slide belonged to, Dr. Banks asked us to guess it. It was interesting how easy it was to see which group was associated with which statistics, which shows how people with certain learning styles tend to veer towards certain academic areas

One interesting thing is that every group (the audience of the workshop, all three faculty groups, students in general), seems to have a strong visual preference which I think is due to the increasing visual stimulus we are all exposed to through television and other “screen” media and computers. Our world is definitely very visual and this has influenced our learning styles. It would be interesting to compare learning styles presently and forty years ago, for example.

Finally, I really enjoyed Dr. Bank’s presentation, which definitely applied his own advice by providing “around the cycle” items. He definitely developed his slides extensively around the visual/verbal category, which is the main one involved in a slides presentation. His strategies for incorporating all the learning styles when teaching seem very realistic and I will definitely apply them when teaching in the future.