2.8+What's+TPACK?

The readings reflections have two main purposes: 1) to hold you accountable for careful reading of and reflection on the readings assigned in class; and 2) to provide you with a record of what you've learned and thought about as a result of the readings.
 * Readings Reflections**

The readings reflections will be evaluated using the following criteria: Submit your readings reflection **before** reading anyone's on the Wiki page and then paste it into the existing reflection page for that current reading.
 * completeness and timeliness of the entries;
 * comprehension of the main ideas of the readings; and
 * depth and quality of integration of the ideas with your own thinking.

For this reflection, please do the following: after reading //Graphing Calculators as Tools//, define what you believe TPACK is. Then briefly discuss its importance for the middle school classroom teacher, giving at least one relevant example of why it is important (from your own experience would be preferred vs just taken from the article). This is due Thursday, March 29, by 8am.

The article, Graphing Calculators as Tools, emphasizes the specialized knowledge needed by middle school mathematics teachers today to integrate technology, pedagogy, and content knowledge (TPACK) effectively into their classrooms (1-4).

In considering learning tools for the classroom, the teacher must carefully consider and assess how technology can impact the learner and the learning process (2-1). The authors do not recommend the use of technology in the classroom in isolation. They establish the framework, TPACK (2-Figure 1), in which technology use can supplement and grow mathematical learning in the middle school classroom. The key to success is to make sure that as teachers utilize technology, they understand how mathematical concepts and pedagogical practices can be integrated with the use of the technology. Students of this generation have been raised on technology and are attracted to it like a magnet. To direct the interest of our students into mathematical reasoning exercises through technology is a breakthrough teaching tool for the classroom.

One example of a technological tool which is useful in helping students to understand the nature of linear relationships is the Calculator-Based Ranger (CBR). The CBR program utilizes the calculator and a motion detector to allow students to physically create different slopes and experience the relationship between rate, time, and distance (2-3,4,5). In utilizing this tool myself at Maple Street Middle School, I witnessed the connections students could make between their walking rate/direction actions and the graph of those actions. The immediate feedback helped my students to acknowledge their misperceptions and correct them (3-4). It also gave me the opportunity to challenge and ask students probing questions concerning rate, time, and distance. My content knowledge in this area was critical in helping to guide the students in understanding the outcomes of their physical actions. This enabled them to build their own knowledge about slope.

In using the CBR to demonstrate the slope of linear equations, it was important that I understood how the technology would support the concepts I wanted the students to master and highlight the misconceptions I suspected they held. The use of the tool mandated lesson organization, teamwork, sharing, and open communication between all participants. All of this had to be accomplished in a very active setting. As the teacher, I planned my lesson on paper but also had to think on my feet as the exercise unfolded. It would have been helpful to have tried this activity on a sample group of students first or to have witnessed another instructor implementing the lesson in order to be better prepared for the unexpected.

I agree with the authors that the use of interactive technological tools can help us teach mathematical concepts in new and meaningful ways to today’s students. Teachers must ensure that when deciding to implement these tools in the classroom, they are integrated in a conceptually meaningful way (5-4). We can not throw technology tools at our students and hope that they have a positivie impact on learning. //**(Susan Copeland) **//

The article TPACK is talking about how since school systems are changing to include technology, teachers need to learn how to use technology to teach in the class room. Graphing calculators can help collect or generate raw data, examine multiple cases, provide immediate feedback, and show graphical and numerical displays (2-3). But it is not just knowing how to use the ideas, it is also knowing when and where to incorporate the technology for it to be one hundred percent effective. This knowledge has been known as TPACK (technology, pedagogy, and content knowledge) (2-4). Teachers must also be able to integrate their understanding of the students math content, instructional strategies, classroom management, and assessment on how technology has an impact on the student and the students ability to learn (3-1). One piece of technology that helps students understand changes in linear relationships is the CBR used with the TI-73. This technology gives the students the ability to see if they are doing anything wrong or have wrong thinking when it comes to graphs. Students can connect meaning to positive and negative slop by walking away or toward the motion detector (CBR) (3-4). One thing I thought was interesting in the article it is talking about having students walk a parabola and they first try to mimic the shape by walking a inverted U to match the graph (3-6). When we were teaching on Tuesday, I had a student try to do that, and even though other people in the group told her it would not work, she insisted on trying it. She was still amazed that her idea did not work. This situation gives students the opportunity to figure out what the graph is showing (4-1). Another application for the calculator is the SMILE, which has the potential to strengthen students' conceptions of angle and angle measurement (4-5). With this application students can watch as an angle is created (5-1). There are many more applications to further student thinking in math, one being a probability simulation (6-1). I really would like to be able to use these applications when I get into the classroom someday. I feel like not only would it further the students understanding of the lesson of choice, but it can also help start a lesson. If a student has no idea what slope is, the CBR might help them start to get an idea on how slope works. I feel like the reason teachers do not use this technology more is because they do not know how to use it. It is no use for the students if the teacher has no idea what they are doing. I really hope when I graduate, I can attend seminars and other activities where I can learn about, and how to use, new technology for the class room. **(Nicole Parry)**

 TPACK, or technology, pedagogy, and content knowledge, is what Browning and Garza-Kling argue our middle school mathematics students need to meet the standards set by the NCTM (481-2), and although one may argue they are "using technology" in the classroom by instructing students to compute with calculators, so much more can be extracted from technology when teachers know "when, where, and how" to use it (481-4).Thus, TPACK represents so much more than what may come to mind when we think of technology, pedagogy, and content knowlege; TPACK requires teachers to combine all aspects of teaching into how they can use technology to best impact students (482-1). Browning and Garza-Kling give several reasons why TPACK is so important through examples of lessons they have fostered, which I am also able to tie into personal experience where I lead a lesson working with 7th graders using TPACK ideals.

As I consider what TPACK truly looks like as a transition from theory to practice, I envision lessons which reflect the standards, push student thinking, and use technology to help students grasp concepts conceptually. As the acronym thus helps clarify, pedagogically teachers must use wise judgement in implementing these tasks as things like group dynamics and appropriateness of lesson for the students could interfere with a lesson. In addition, strong content knowledge must also be in the formula for TPACK because teachers must decide what information students need to learn for the experiments, when forming them, to decide if students are actually learning. Lastly, technology has many benefits when used in the right manner that textbooks cannot present students. Browning and Garza-Kling provide examples on what a TPACK lesson looks like, and, given our focus in class on the CBR program, we will investigate how this use of technology follows the TPACK philosophy, both through the author's argument and my own experience.

Browning and Garza-Kling claim one benefit to their use of the CBR motion detector in helping students learn about slope is that student can "physically investigate the nature of change in linear relationships" by walking (482-4). This, as the authors point out, has a number of benefits including giving students a real example of an "m" value and "y" intercept (484-5), recognize the steepness of a graph (482-6), and discover positive, negative, and no slope (482-6). When working with students completing a lab with this technology, I noticed that students truly were realizing these things-- that if they walked away from the motion detectors the graphs increased, if they stood still there was no slope, and so forth. My difficulty came with what Browning and Garza-Kling suggest a crucial element to these lessons: "students providing a mathematical argument as to why" (482-7).

The students I worked with struggled to make the connection with slope to this activity. Constantly, the viewed the graph as a hill, even after preforming the activity. I struggled fostering discussions which would focus students' attention on connections, but they were struggling to draw the connections I desired. Thus, with these activities, I believe teachers must be well prepared for student misconceptions in order to help them arrive at the desired understandings-- I can see where these types of lessons can transition from educational to recreational quickly if not fostered correctly; thus, all elements of TPACK must be meet for lessons like those offered by the authors to reach their potential: helping students better understand mathematics. (Katie)

I believe that TPACK is a way to help guide teachers towards a better understanding of technology, when it should be used, and how to best use it. I think this because it stands for technology, pedagogy, and content knowledge, which leads me to believe that TPACK is a way to help teachers teach their classes, while including technology into their classrooms. TPACK is important for any math teacher, but especially for middle school, because there is a big push to incorporate technology into schools. Middle school is the time when students need to be introduced to using technology, while gaining a solid, conceptual understanding of math, so they can carry that into high school and be prepared for the courses there. TPACK is important then, because it gives the teacher a reminder of things to think about when planning a lesson and how it is going to be run. Some questions to ask ourselves before we use technology in the classroom are: How is the technology going to be used, is it going to be beneficial, and how will it affect the atmosphere of the classroom? From my lessons in KPS, I know that understanding the why technology is being used, and the how it will be used, are important. Otherwise, you will be stuck high and dry trying to make it through a lesson that you're not sure what to do with. TPACK shows that we need to plan ahead of our lessons, so we know whether the class will benefit from the technology or not, and whether the technology is appropriate for that lesson. My lesson at Maple Street is a good example of this, because I had to plan ahead what graphs I wanted the students to walk, what I wanted them to learn, and how I wanted them to learn it. This meant that I had to plan ahead, and understanding TPACK allows us to plan these lessons and keep them under control, so we can run an effective classroom.-Josh Kaylor


 * __ Graphing Calculators as Tools __**

The school system and content within it are constantly changing, especially with technology. There are new advances that help teachers educate their students with better understanding. graphing calculators are especially popular nowadays, since they are relatively affordable, portable, easy to use and have extreme functionality (481-3). The knowledge necessary to use technology effectively in the classroom is known as TPACK (technology, pedagogy, and content knowledge) (481-4).

TPACK requires teachers to know how to integrate technology in such an effective way that allows the students to absorb the information in the best possible way. The article by Christine Browning and Gina Garza-Kling also mentions motion detectors as being a very useful tool in the middle school mathematics classroom (482-3). They allow the students to physically demonstrate the graphs they are studying, and investigate how it relates to real-life situations which make it easier to learn the concepts. The students can also explore the ideas of positive and negative slope when walking towards or away from the motion detector.

The SMILE application allows students to put mathematics knowledge into everyday life, such as knowing the angle of a snowboarding trick, rather than knowing the strict definition of angle but not truly applying it to their life (484-1). It helps them grasp the concept of angles and be able to really visualize them, rather than only knowing what they mean on a paper drawn out specifically correct.

Another aspect of middle school mathematics that the article points out is probability, and how that can be effectively taught with the use of technology. Probability simulators on TI-73 calculators can generate a lot of quick results (485-2).

Overall, the article outlines how the use of technology such as graphing calculators can greatly benefit students in the classroom. Such advances allow for kids to grasp a better overall understanding of concepts since they can visualize and physically experiment with them. In my opinion, I agree with the article because the more you get the students involved, the more they learn. Techlology enables them to grasp lessons through hands-on activities that really interest them. (**Shanna Thorn**)

In //Graphing Calculators as Tools//, attention is brought to the importance and practical nature graphing calculators play in the classroom setting. One cannot simply use graphing calculators in hopes that the students will have a learning experience. Instead, knowing the time and place of a lesson to integrate such technology can be an effective way of teaching and learning mathematics (1-6). TPACK (teaching, pedagogy, and content knowledge) is key to integrating technology in the classroom successfully. The TI-73 is a focus of the article; however, many other calculators have access to the applications either from the internet or from another calculator via a transfer link (2-2). As Figure 1 shows on Page 2, TPACK is the intersection of teaching, pedagogy, and content knowledge. Therefore, a teacher will need to utilize all three in order to have their successful implementation of technology into their lesson.

Texas Instrument’s TI-73 with the CBR or CBR 2 motion detectors allow students to graph data instantly and then can use their data in graphs to test out concepts such as distance, time, and rate (2-5). From my own experience in using this with some 7th grade students, I know that this brings a whole new world of math into the hands of the students. Touching briefly on this, the 7th grade students I worked with wanted to test different speeds at which they walked to or from the CBR, make exponential slopes, and make stories that they would hypothesize what it would look like and then test that hypothesis. These tools are great for helping students understand such algebraic concepts easier than without such technology.

Geometry is also another topic that these calculators can help students discover. The SMILE application of the TI-73 allows students to see, manipulate, and estimate different angles, up to 360 degrees (3-1). This application is also a way for students to get immediate feedback and make improvements where a textbook or paper and pencil are not able to give such feedback (3-8).

There are also applications for probability scenarios of the Texas Instrument systems. Such simulations as coin toss, rolling dice, drawing cards, and others offer a whole new dynamic stimulation to students (4 - Fig. 4). I know that these applications do not simply generate the result and leave it at that, but they also provide histograms that allow students to statistically analyze their findings using these applications.

Graphing calculators have so much more potential than just computations. These can be used as strong tools that visualize mathematics and put it in the hands of students. Teachers must know how to first use the technology so that they can effectively use it to aid in their lesson(s). As TPACK is defined, a teacher must incorporate their own pedagogy and content knowledge into the use of technology in their own way. The article gives a few examples of how graphing calculators can be used, but every teacher should be creative and bring this technology into their classroom in their own way. **(Ryan Sherman)**

===TPACK which stands for Technology, Pedagogy, and Content Knowledge is the idea of fully integrating technology into the learning process. A teacher can’t just throw technology into their classroom based on their personal knowledge and proficiency with a piece of technology; they need to combine all of their knowledge of what is going on in the classroom such as classroom management, instructional strategies, student tendencies, and assessment (3-1). By considering all of these pieces in the classroom a teacher can have a better perception of how the technology will impact the learning process and students. This goes along hand in hand with a lot of the ideas characterized in //Principles and Standards for School Mathematics// by providing new interactive ways of exploring mathematical ideas (2-3). There was a good example of this in the lesson I taught on Tuesday where I had my students try to tell me what the graph we drew meant, I had given them a graph similar to what they were about to see with the CBR. Even though we had the graph labeled with the x-axis being time and the y-axis being distance the most they could do was read off the coordinates to me, but after a while of experimenting with/using the CBR in the hallway they were starting to understand just what the graph meant. After we returned to the classroom I asked them once again about the graph and this time they told me step by step what the graph indicated by going over how they could walk it to get the same graph. This particular experience opened my eyes a bit more to exactly how this technology effects student learning where before coming from a college students view point of already having the knowledge of these concepts I saw the CBR as more of a hook to get students to pay attention and be more interested. -**HUTCH** ===