Welcome Calculus and Geometry Students!

This is Mr. Baumgart’s class blog. On this site, I will post the geometry notes, assignments, and daily schedule. Simply click on the geometry link above to access these items.

If you are an AP Calculus student, I will typically post solution guides to problems and/or any important documents for you to utilize.

Have a fantastic semester!

Mr. B

Attention Calc BC! (Revised)

I hope you all are enjoying the weather and studying hard! I have posted the solutions to the review in the normal spot within the CalcBC link. If you have any specific questions that are not covered by the review, feel free to shoot me an email anytime today.

You should hear about a new exam schedule shortly. Check with the district website. I do know we are not having the Calc exam tomorrow!

Good luck,

Mr. B

Reflecting on my GAME plan

EDU6713: Course Reflection

Over the past seven weeks of this course, I have learned a great deal while implementing my GAME plan. My original plan was to spend at least an hour every two weeks researching a technology that I could use to accentuate my lessons. I later decided to research weekly instead of biweekly since I enjoyed it so much and was eager to learn more.

I spent a solid month studying the Geogebra mathematics application and brainstorming ideas for using it my classes. I ended up redesigning an entire calculus lesson on vectors due to the amazing visuals provided by this app. I also plan on utilizing Geogebra heavily in my geometry classes next year since nearly any geometric structure can be created and experimented with by students. While I studied a number of mathematics technologies I was not crazy about, the other promising program I spent some time with was Winplot. Ever since I began teaching AP calculus, I wanted to find a way to make solids of revolution come to life for my students and Winplot is the application that does it. The learning curve was a bit higher for this program than for some of the other graphing technologies, but it is the only one I found that adequately shows the result of revolving solids around an axis of rotation. I will need more practice with this one before I am ready to incorporate it into my lessons, but I already anticipate using some summer time for this purpose.

Due to the positive results I have seen in my instruction as well as my own motivation through implementation of my GAME plan, I intend to continue building my technological repertoire even after this course ends. I feel like the pace of research I set is reasonable so I do not intend to revise it at this time. I also intend to share the GAME format with my students in order to improve their creative and self-directed learning skills (Cennamo, Ross, and Ertmer, 2009). Therefore, at the beginning of the unit plan I developed this year, I will introduce the GAME format to my students so they may use it to set goals, plan their project, monitor their progress, and evaluate their performances. Since it will be my first time utilizing this process, I will likely develop a project sheet the students will complete at the end of a work day to self-assess their performance.

Some of the learning I acquired in this course will be utilized immediately while some will have to wait a year before it is implemented in my classroom. As far as immediate application goes, I plan on giving my Calculus students the opportunity to do their final lesson by utilizing digital storytelling. The students will have to teach a Calculus lesson and a digital storytelling program is a nice way this can be done. I already utilize the social networking aspect of technology through Edmodo and I do not have an additional plans for this platform at the moment. In terms of problem based learning, I will have to wait another year to implement the full unit plan I developed in this course. However, I was excited with how well the first lesson based on problem-based learning turned out and cannot wait to see how the other two follow up lessons will play out.



Cennamo, K., Ross, J. & Ertmer, P. (2009). Technology integration for meaningful classroom use: A standards-based approach. (Laureate Education, Inc., Custom ed.). Belmont, CA: Wadsworth, Cengage Learning


Stepping up my GAME

It has been two weeks since I established my GAME plan. In my original plan, I decided to devote one hour at least biweekly researching and noting digital tools I can use to upgrade some of my lessons. Each month, I plan on using one of the tools I studied to revamp an entire lesson. Therefore, if all goes according to my GAME plan, I will have twelve new, technology-rich lessons to share with my students.

This week, I continued my exploration of Geogebra, a popular mathematics application. I commented in one of the discussion posts that I was particularly excited with the way this technology handled vectors; so impressed in fact, that I have decided to add this technology to my AP calculus lesson on vectors for next year. It can certainly help my students to see the actual vectors (position, velocity, and acceleration) after we have used calculus to derive them.

In response to the questions this week, I had no problem finding information and resources concerning Geogebra. Although I downloaded the user’s manual, I have found the online tutorials that exist all over the internet much easier to follow.

The only modification I will make to my GAME plan is to intensify my research. Rather than explore a new technology biweekly, I will attempt to do this at least once a week. I believe my original plan on modifying one lesson a month, however, remains a realistic goal; therefore, I will not be altering my strategy for this portion of my GAME plan.

As I explore Geogebra, new questions abound. For instance, how could I use it in my geometry classes? There are of course a number of features in the application that are applicable toward geometry as well. Also, what is another technology to explore after I have researched the limits of Geogebra? For this question, I reach out to my colleagues since this is where I heard of Geogebra in the first place.



Monitoring my A(ctions)

In this week’s post, I will be discussing the progress I have made thus far in the implementation of my GAME plan. This week, I used a conference hour, as per GAME plan, to explore a potentially useful digital tool known as Geogebra. I got the idea to explore this technology from our most recent teacher inservice although I had previously heard good reviews. I downloaded the app on my Ipad and played around with some of the features for around an hour. Having just completed a lesson on vector calculus, I was dismayed to find that I could have really used this app to display all of the important vectors (position, velocity, and acceleration) precisely during my lesson! Following my exploration, I immediately logged Geogebra into my spreadsheet of potential technologies and noted its potential use during this lesson next year. There were many other features of this app that had promise as well, so I will likely spend some additional time with this tool.

To continue with my game plan, I will read the tutorial on Geogebra built into the application in order to learn how to use it properly. I may also seek out some online tutorials since I often learn better from them than from reading alone. Unfortunately, while a colleague introduced this tool to me, she herself had not really done much more than toy around with it either. Perhaps some of my fellow math teachers reading this blog have used it before and could offer some tips?

My GAME Plan


In this assignment, I chose to focus on the following two ISTE (2008) indicators from which to further develop my confidence and proficiency:

  • 2(a) Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity.
  • 5(c) Evaluate and reflect on current research and professional practice on a regular basis to make effective use of existing and emerging digital tools and resources in support of student learning. (ISTE, 2008)

To become proficient in these two indicators, my long-term goals will be to do regular research on new digital tools, and then use them to enhance or even replace some of my existing lessons. To put this plan into action, I will follow a strict timeline:

  • At least biweekly, I will spend one conference period or take on hour after school to research new digital tools that could potentially be used to create new learning experiences for my students.
  • At least monthly, I will either incorporate the technology into a previous lesson, or design a completely new lesson with the new technology in mind as well as the relevant content standard.

To monitor my plan of action, I will keep Microsoft Excel to keep digital log of my research in which I note the new technology, give a brief synopsis of it, note the url where I found it, and write a summary of its potential use in a lesson.

At the end of each month of research, I will either restructure a lesson utilizing one my newly found digital tools, or design a new learning activity where students could use it to teach themselves the content. Lesson adjustments will be recorded in my plan book and then performed either this year or next. Once the lesson is executed, I will take the advice of Cennamo, Ertmer, and Ross (2009) and keep a digital reflective journal using PlanBook so that I can assess the overall effectiveness of the lesson and technology that was utilized. I will also be sure to design a formative assessment for each new lesson so that I can monitor the progress of my students and be sure they are in fact learning.

To evaluate and extend my own learning, I will use the reflections from my plan book to make further adjustments to each lesson so that they become better each time they are executed. I will also be mindful of new digital tools that may crop up and possibly be better alternatives than the one currently in use. Finally, I will seek out any professional development which may further extend my proficiency of these two NSTE indicators (i.e. those that focus on digital tools and accompanying learning environments).


Cennamo, K., Ross, J. & Ertmer, P. (2009). Technology integration for meaningful classroom use: A standards-based approach. (Laureate Education, Inc., Custom ed.). Belmont, CA: Wadsworth, Cengage Learning.

International Society for Technology in Education. (2008). National education standards for teachers (NETS-T). Retrieved from http://www.iste.org/standards/nets-for-teachers





Final Reflection: My Personal Learning Theory

My personal learning theory, developed in week one of this course is as follows:

I believe students learn through a chain reaction of experiences. The knowledge acquired through a given experience can then be connected to a new idea, which can then be learned by drawing on the learner’s previous experience.  Transfer occurs via a student’s immersion within a given learning experience. Learning is therefore like a set of dominoes, where each domino represents a given experience, and each is necessary to “knock over” the next.

After taking this course, I still stand by my original description. According to Orey (Laureate Education Inc., n.d.), learning theories consider what transpires in the learner’s mind during the learning process and assume that the learner is actively involved during the process. My theory was written with these ideas in mind and I do not believe any further modification is necessary.  What I have learned, however, is how to use technology to create or accentuate the learning experiences my students will use to gain knowledge.  I believe this was the ultimate purpose of the course: to begin a lesson with how the learning is going to happen and then use technology to either create the necessary experience or to add depth to it.

I certainly feel this course has expanded my repertoire of instructional skills. While I would say I was fairly adept using most of the nine instructional skills described by Pitler, Hubbell, and Kuhn’s Using Technology with Classroom Instruction that Works, I learned many possible ways to enhance the skills through technology usage. What I would like to do in the short term with my newly acquired knowledge, is to add technology to some of my previously designed learning experiences.  Two such experiences that come to mind will be approaching shortly in my geometry courses. After we have studied quadrilaterals, I typically give the students a blank graphic organizer in which they list the theorems related to each quadrilateral. To enhance this idea with technology usage, I will have the students create the organizer (with some guidance of course) themselves using Inspiration or any other free organizing software. In another upcoming lesson on slopes, I would like to add motion sensors to the lesson in order to model constant speed situations. My students would then have to interpret the meaning of the slopes of the lines the made after they had a good old kinesthetic time creating the graphs. These real-life connections to math are missing from far too many of my lessons.

In the long term, I would like to add at least one lesson per unit to my courses where students use technology to experiment, make predictions, and experience a real-life connection to the mathematics they are learning. My motivation is not simply due to Pitler, Hubbell, and Kuhn’s (2012) assertion these students will attain a deeper understanding of lesson concepts (p. 204), but because this type of thinking is the foundation for mathematics and science in general and should therefore be part of the curriculum. Accomplishing this goal will take planning and collaboration with other teachers in order for them to buy into this notion. It would also likely require some curriculum trimming to ensure we have the time to perform the activities, but it should be a realistic goal to attain. If two of these lessons can be added per year, it shouldn’t take long to ensure that I have a scientifically minded student population leaving my classroom in the summer. I would certainly feel better about my teaching if I knew this were happening. With some time and work, it will happen.


Laureate Education (Producer). (n.d.). Instructional theory vs. learning theory [Video file]. Retrieved from https://class.waldenu.edu

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.


Social Learning Theory and Technology (Voicethread url included)

This week at Walden University, the focus is on social learning theories, in particular, social constructivism. According to Orey (n.d.), social learning theories describe learning as the result of artifact creation through social interactions (Laureate Education Inc. ).

The instructional strategy examined this week, was cooperative learning. By its very nature, cooperative learning is clearly grounded in social learning theories.  Since students in well-constructed cooperative learning settings are engaged with others as a product is created, Orey (2001) claims that meaningful learning will occur (Assumptions of Social Constructivism Section, para. 4).  Piter, Hubbell, & Kuhn (2012) describe cooperative learning as an environment focusing on student interactions that facilitate their learning (p.73). This sounds remarkably similar to the primary philosophy of social learning theory that was previously described.

Pitler et al (2012) go on to describe a number of technological settings in which cooperative learning can occur. Student multimedia projects, in which students work together to create video or animated films, can be designed so that a group of students can each have a role in the finished product (p. 75). Technology also enables cooperative learning even when it is difficult for students to meet in groups during school hours to work on their projects. Students can use platforms such as Skype, Facetime, (p.80) or even multiplayer simulations such as The Sims (p. 85) in order to interact outside of the classroom.

Thank you for reading my post this week. You can access my VoiceThread for the coming application at:   https://voicethread.com/new/share/6104418/





Laureate Education (Producer). (n.d.). Social learning theories [Video file]. Retrieved from https://class.waldenu.edu

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. Retrieved from http://epltt.coe.uga.edu/index.php?title=Main_Page

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.



Contructivist/Constructionist Learning Theories and Technologies


According to Constructionist theory, optimal learning takes place when a student creates an artifact that can be shared with others. The basis for Constructivist theories, on the other hand is that individuals actively construct their own meaning of things (Laureate Education Inc. n.d.).  The important point both theories make is that the learner is an active creator of something that is their own. A project-based learning (PBL) environment is one where these two similar theories of learning come to life.

In this week’s learning resources at Walden University, I explored a higher-order instructional strategy known as generating and testing hypotheses. For students in a PBL environment, this will be a key skill students will need to possess since inquiry is such a critical component of PBL (Orey, 2012), and therefore, Constructionist learning. Any science teacher understands that inquiry is intimately connected to hypothesis formulation and experiments designed to test them.

Pitler et al (2012) describes several instructional technologies conducive to Constructionist theories and hypothesis generation and testing including premade spreadsheets, data collection probes, and web-based interactives. All of these strategies allow students to experiment in controlled environments and test the validity of their hypotheses. Spreadsheets allow students to manipulate large amounts of data and make predictions based on the data (Pitler et al, 2012, p. 208). Probes can obviously be used to gather data quickly, safely, and efficiently and allow students to easily verify or refute a given hypotheses. Similarly, web-based interactives, including one of my favorites, explore learning gizmos, allow students to run physics and chemistry simulations to test their conjectures as well (Pitler et al, 2012, p. 219).  Needless to say, such technologies fit into a PBL environment nicely.

Laureate Education (Producer). (n.d.). Constructionist and constructivist learning theories [Video file]. Retrieved from https://class.waldenu.edu

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. Retrieved from http://epltt.coe.uga.edu/index.php?title=Main_Page

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.

Cognitive Instructional Strategies


In this week’s course resources, Dr. Michael Orey describes four components of various cognitive learning theories including limited short term memory, elaboration, Pavio’s dual coding hypothesis, and a network model of memory (Laureate Education Inc., n.d.). In this post, I will be discussing how the instructional strategies studied this week in Pitler, Hubbel, and Kuhn’s Using Technology with Classroom Instruction that Works align with cognitive learning theory.

The first instructional strategy studied was the use of cues, questions, and advance organizers. According to Pitler et al (2012), all three of these strategies focus on “enhancing students’ ability to retrieve, use, and organize information”. According to cognitive learning theory, elaboration builds connections to stored information, and the more connections that are made to a piece of information, the less likely it is to be forgotten (Laureate Education Inc., n.d.). Since advance organizers, questions, and cues are often framed around essential questions that attempt to make connections between prior knowledge and the knowledge to come, they are basically elaboration tools. It should also be noted that many of the organizing technologies, such as Inspiration, also mimic the nodal, or network model of memory described by cognitive learning theory.

The second strategy, summarizing and note taking, is certainly a cognitive tool. One of the clear purposes of note taking is to provide students with a visual reference to the information discussed in class. Since the information learned in class typically exceeds the seven or so items the brain can store into short term memory (Laureate Education Inc., n.d.), notes provide a way to access the information that is lost following instruction. Pitler et al (2012) also claim that combination notes consisting of “outlining, webbing, and pictographs, in addition to words” (p. 151) is a particularly strong note taking method. Cognitive learning theory explains why this is so. Pavio’s dual learning hypothesis states that information is stored in multiple ways, usually as images and text (Laureate Education Inc., n.d.); it therefore makes sense that that combination notes are so powerful since they include a representation of pictures and texts thereby making the information more likely to be stored into long term memory.



Laureate Education (Producer). (n.d.). Cognitive learning theories [Video file]. Retrieved from https://class.waldenu.edu

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.