The Views of High School Geometry Teachers regarding the Effect of Technology on Student Learning
Honors Thesis Final Project April 2012 Melanie Lolli
Ohio Dominican University
Dr. James Cottrill Dr. Marlissa Stauffer Dr. Matthew Ponesse
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The Views of High School Geometry Teachers regarding the Effect of Technology on Student Learning
The National Council of Teachers of Mathematics claims that technology is necessary to student learning in math and, in fact, enhances it. There are some studies to support this claim, but these studies leave some unanswered questions. The purpose of this study was to find out from current high school math teachers, of geometry specifically, what their views of technology are. The goal of the study was to ask these teachers which technologies they use and whether they believe technology has beneficial effects on student learning. Data was collected for the survey by asking teachers to take brief electronic surveys and conduct in-person interviews. All questions in both the survey and interviews were focused on the effects of technology that they see in their classrooms. The scope of the participants was restricted to Columbus, Ohio, and thus, generalizations for any classroom or any school building cannot be made. However, this study did find a consensus among the participants as to which technologies they felt were the most beneficial in their classrooms, as well as those that might not be needed at all in a classroom. The three technologies that these teachers claimed to be the most beneficial were SMART boards, TI-nspire calculators and Geometer’s Sketchpad/GeoGebra. Again, this study cannot make solid conclusions, but it is safe to say that this study gives insight into teachers’ viewpoints, which, in a sense, are more important than those of outside researchers. The teachers agreed on a few technologies that are the most beneficial and thus future studies should focus on really studying the effects of these technologies as well as focus on getting a wider range of teachers’ opinions on this topic.
Technology is a major driving force of today’s world. Businesses and individual jobs depend on technology to function properly, most all forms of communication use technology, and entertainment is found more often through technology than not. Since technology is such a large part of the current world, it would seem that technology should be incorporated in school classrooms. The National Council of Teachers of Mathematics has determined six principles, which describe aspects of high-quality mathematics education. One of these principles states that
“technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students’ learning” (NCTM, 2000). The claim is Lolli 3 that technology is essential to learning and that it enhances it. What research has been done to support this claim? Several studies have explored technology in geometry classrooms and its effects.
A few studies have shown positive student attitudes towards geometry when using technology. Charles Funkhouser observed and tested students in two classrooms; one with computer-augmented instruction and one without. He found that the students’ test scores in the computer-augmented instruction classroom were better, and according to surveys, the students’ attitudes toward geometry changed for the better (Funkhouser, 2002). Another study found that using an open-ended learning environment, where students have more power over their own learning, in conjunction with dynamic geometry software led to positive attitudes of students towards learning geometry (Hannafin, 2001).
In addition to students’ attitudes towards technology, teachers’ attitudes towards technology have been explored by several studies. In open-ended learning environments, teachers need to accept the role of facilitator and supporter. Hannafin found, with his research using dynamic geometry software, that teachers have a hard time relinquishing their control of the classroom because they feel responsible for their students’ learning (Hannafin, 2001).
Another study found that the motivations of teachers to use technology are often personal and not focused on the needs of the students. Incorporating technology into lessons requires more time for planning a lesson and often more time executing the lesson. Implementing technology in the classroom also requires training and support for teachers (Holden, 2008). This same study found that teachers can see the benefits of incorporating technology but are neutral on whether technology affects in-class activities (Holden, 2008). Lolli 4
Bryan Dye led a study implementing a particular dynamic geometry program into 10 classrooms and observing the effects. Dye had found previously that teachers find it difficult to incorporate dynamic geometry programs in their classroom because it takes a long time to teach the students how all the symbols and icons are associated; it often turns into a technology lesson instead of a geometry lesson. However, with this particular program, Dye found that teachers were surprised that it was not just a computer lesson; more math learning took place than they expected (Dye, 2001). Another study explored teachers’ attitudes and beliefs of technology and how those beliefs affected the teachers’ use of technology in their classrooms. The reasons a teacher uses a new technology include how useful they think it will be, how easy it will be to use, and if it is compatible with existing technology. Whether they use the technology also depends on the expectations of colleagues and parents as well as the extent of support they have from technology staff. The study concluded that to understand why teachers use the amount of technology they do, it is necessary to take into account their individual pedagogical beliefs (Stols
& Kriek, 2011). Stols and Kriek also stated that “further investigations should focus on how and for what purpose teachers used dynamic geometry software in their classrooms” (Stols & Kriek,
2011).
In 2010, Grunewald and Associates presented an article titled, “Educators, Technology and 21st Century Skills: Dispelling Five Myths.” First, they found that teachers do not believe that they were well prepared to incorporate technology during their pre-service education classes.
Also, teachers and administrators often disagree as to how much technology incorporation is occurring. Teachers find that all students, including high achieving students, students with academic needs, and ESL learners, benefit from technology use. Grunewald and Associates also found that veteran teachers and new teachers are equally likely to support technology in their Lolli 5 classrooms; teachers that are not using technology believe that it is not necessary for their lessons and not because they do not know how to use it. And finally, this report found that teachers who frequently use technology state good effects on students; the students learn how to use technology more effectively (Grunewald and Associates, 2010).
Studies have determined whether students and teachers like a specific technology for geometry as well as why teachers use technology or not. However, it has yet to be determined which particular technologies, out of those available to schools, geometry teachers believe are the best to be used in their classrooms. Do certain technologies enhance learning in geometry?
Are these technologies essential to teaching and learning geometry? The purpose of this study is to gain the opinions and views of teachers who have first-hand experience with technology in a high school geometry classroom.
Obtaining the views of teachers regarding effects of technology in the classroom is important because they are the ones that witness first-hand the effects a technology has on students. Several teachers will have taught the same lessons with and without certain technologies. Thus, they will be able to compare whether the lesson was enhanced with the incorporation of technology, the technology had little or no effect, or the technology was actually detrimental to the lesson.
Researchers and investigators can only see so much when they observe a classroom for a month or even a year to ‘test’ the effects of a particular technology. Teachers, on the other hand, are in their classrooms every day of the week and know their students the best. Thus, they will be able to more effectively judge which technologies have better effects on student learning. This study will also be beneficial because these teachers will be able to compare a vast list of varying technologies and report which one(s) they believe have the best effects on student learning. As a Lolli 6 result, schools and researchers will be able to see which technologies to focus on for further study and possible implementation in classrooms.
Methods
The participants of this study were high school geometry teachers in public, private, and charter schools in Franklin County. The teachers were asked if they wanted to participate and if they agreed, they were sent an online survey. The survey asked these teachers to evaluate the effects of various technologies on student learning and determine which one(s) they believe to be the most beneficial. Student learning was defined as engagement in class, ability to recall information, ability to apply information, and performance on in-class assessments. The last question of the survey asked if the teacher would be willing to discuss his or her ideas and opinions further via an in-person interview. After the surveys were completed, those that agreed to a further interview were contacted and an interview time was set up.
With the use of three websites, “Franklin County Charter Schools,” “Franklin County
Private Schools,” and “High Schools in Franklin County, Ohio,” a list of 60 high schools in
Franklin County was compiled (see Appendix A). From each school’s website, the main information email address or the main secretary’s email address was obtained. An email was then sent to each school with a brief explanation of this study and requesting for the name(s) and contact information of the geometry teacher(s) at the school.
Email responses were received from 16 of the schools with contact information for a total of 38 high school geometry teachers. A second email was then sent to each of these teachers explaining the goals of this study and asking them to respond if they were willing to participate in the online survey. Twenty-four teachers responded saying they would be willing to participate.
These teachers were then sent a link to the survey which was created using SurveyBuilder.com. Lolli 7
The survey consisted of two sections: the first was for the purpose of creating a comprehensive list of technologies the participant currently uses or has used in the past; the second part consisted of 12 questions that asked the participants to evaluate the effects of the technologies that they had listed as having experience with. Most of the questions in part two only required a yes or no answer or a fill-in-the-blank answer using the names of the technologies from Part I.
Some questions asked for a short answer/explanation but these were optional for the participants to answer (see Appendix B). The participants were asked to complete the survey within a 2-week period. The following pie chart shows the demographics of the teachers who said they would be willing to complete a survey.
The surveys were briefly analyzed as they were being completed. The analysis showed that most all of the questions were yielding beneficial answers. However, because a survey cannot ask follow-up questions, there were still unanswered questions. After all the surveys were completed, there were seven participants in favor of doing an in-person interview. These teachers were contacted and interviews were set-up with six of them (for questions used in the interviews, see Appendix C). The interviews lasted between 10 and 20 minutes. An audio recording device was not used, but notes were taken and paraphrased transcripts were written up within an hour after the interviews were conducted. The demographics for the interviewees were as follows: three taught at parochial schools, two at suburban public schools, and one at a charter school. Lolli 8
Results
The results of this study are organized here into three major sections. First, one will find a compilation of data responses on some specific types of technologies. These include responses on calculators, presentation devices and dynamic geometry software used in geometry classrooms. Second, there is a short discussion on miscellaneous aspects of using technology.
This section includes responses of technology use outside of the classroom, incorporating technology into project-based learning, as well as the availability of training for new technologies. The third and last section reveals the participants’ positive and negative opinions of technology use in general as well as effects of specific types of technology. Included in this last section are teachers’ opinions on the major questions this study sought to answer: What technologies should be used most often and which technologies have positive effects on student learning?
1. Specific Types of Technologies
Scientific and Graphing Calculators
The first question on the survey was whether calculators were used in the participant’s classroom. Out of 22 responses, 21 said their students did use calculators. Eleven participants said they used TI-83 and/or TI-84 calculators, followed by eight using scientific calculators and six using the TI-nspire calculators. A separate question asked what technologies the participants believed to be beneficial to student learning. Out of 20 responses, five of them said TI-nspire was beneficial. Yet another question asked if the teachers could pick one technology they believe to be the most beneficial to student learning of geometry and out of 19 answers, four said calculators in general were the most beneficial. Lolli 9
During the interviews, the participant was asked what calculators were used in their classroom and how they were used. One teacher said that her students are able to use calculators and they have to bring them to class from home. Some students have TI-30’s and others have TI-
81’s and TI-82’s. Still others just use their cell phones. She also said that the students really don’t use their calculators for anything specifically related to geometry (Interviewee 4, personal communication, December 14, 2011). Another teacher said she uses the TI-30XIIS calculators with her students, which are the calculators required for use during the OGT. She said the students can use them on anything but they are not allowed to approximate. She urges students to always answer with a precise number (i.e. 2*sqrt(2) instead of 2.82843). She also does not use the calculators for anything Geometry specific (Interviewee 3, personal communication,
December 12, 2011)
The brand new TI-nspires are beginning to be used by several school districts as the survey showed. Two of the teachers interviewed had just started using them with their students this year. One teacher said that her students have only used them a few times so far this year to create simple constructions and do a couple explorations. She thinks the TI-nspires are definitely helpful for the students. She doesn’t believe they are essential in learning geometry, but seeing and drawing a figure and then immediately seeing the algebraic representation of what they drew makes connections easier to discover for students (Interviewee 5, personal communication,
December 15, 2011). A second teacher believes the TI-nspires are fantastic. Not all students have them yet, but her school has a loaner program, which she says is what a school would need for the students to make the transition to these calculators. She hasn’t had as much experience with the TI-Navigators yet (the software used to connect every student’s calculator wirelessly to the teacher’s computer to easily transfer information), but she cannot wait to use the Navigators Lolli 10 because of the ability to get instantaneous feedback. (The navigators allow the teacher’s computer to send out questions to each student’s calculator and then retrieve and store each student’s answer, similar to ‘Clickers.’) She also believes the explorations available with the TI- nspires are great for the students; it was difficult to use graphing calculators in geometry before but now the geometry is right in their hands. She has done constructions with her students and she believes the TI-nspires are better than using Geometer’s Sketchpad. She also claims that these calculators are the most beneficial technology she uses in her classroom. In addition, she feels that she does not have to do as much planning with the technology because she can ask the students if they are able to do something on the calculator and then they can explain it to her; the students are so good with this technology. She believes that if a student can explain and teach a concept to somebody else, he or she is learning it better which is what often happens with these
TI-nspires (Interviewee 1, personal communication, December 7, 2011).
Presentation Devices
The survey asked participants to identify what technologies they use for presentation or lecture and to check all that they use. Top answers included the SMART board (19 responses), the overhead projector (17 responses), and a digital projector connected to a computer (14 responses).
SMART board
Out of 20 survey responses, nine said the SMART board is the technology they use most often and seven said they believe the SMART board is the most beneficial technology they use in their classroom. Four of the teachers interviewed use a SMART board on a daily basis.
One of the interviewees says she enjoys using the SMART board primarily because it is nice being able to prepare ahead of time instead of having to write something out for the Lolli 11 students. It is also nice to be able to save work done on the SMART board and sometimes post the files or worksheets online (Interviewee 2, personal communication, December 7, 2011).
Another teacher said she uses the SMART board everyday in her classroom, mainly to display
PowerPoints she has put together. Students also come up to the SMART board on a regular basis to work through problems (Interviewee 4, personal communication, December 14, 2011).
One teacher claimed that the SMART Board is much better than a chalkboard and she says she will never use a chalkboard again. The students come up and use it sometimes, especially when she needs help with it; she said they are jumping at the chance to use it.
Although she uses it as a presentation device most of the time, she does have pre-made examples and shapes that the students can come up and manipulate (Interviewee 1, personal communication, December 7, 2011).
The fourth teacher I interviewed said she uses a SMART Board and it is her ‘best friend.’
She started using it seven years ago and before that she just used the overhead projector. She also uses a tablet computer along with the SMART board so she can sit facing the students while she is talking through examples and notes. She thinks the most helpful aspect of the SMART board is the fact that the teacher can save notes, which students can then request later, she can post online, or she can email directly to the students. She also feels that the overhead projector was more intimidating to students, and a lot more students feel comfortable coming up to the
SMART board to work through a problem than they did with the overhead projector. She claims that this is the most beneficial technology she uses because it is the most accessible to the students.
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PowerPoint and Elmo
PowerPoint slideshows and the Elmo Document Camera did not come through on the survey as very widely-used presentation devices, but the other two teachers I interviewed, apart from the four above that use a SMART board, both strongly believe that these two presentation devices are important in a geometry classroom.
One teacher uses a PowerPoint slideshow almost everyday to introduce new material and to review old material. He says that he likes PowerPoint for the fact that he can review so quickly by jumping through the slides the students have already seen a few days ago or even a few weeks ago. He also loves that it is dynamic and has GeoGebra capabilities. He is able to create a figure on GeoGebra or an animation and then do a screen capture or a video capture and insert it directly into his PowerPoint. He believes PowerPoint is the most beneficial technology he uses (Interviewee 6, personal communication, December 16, 2011).
A different teacher uses the Elmo as her presentation device. She has the students participate by coming up to the Elmo and demonstrating a problem, talking through it, teaching it to their peers. She strongly believes that the students who are teaching understand the concepts even better themselves. She said that it is about taking ownership for their learning. It is easy to sit back and watch somebody do a problem for them. But if they can do it themselves and then present it, they will learn it that much better. Having the students present to the class is great for them to figure out their own thinking processes. They often begin to say something, catch themselves, and figure out the right answer all on their own (Interviewee 3, personal communication, December 12, 2011).
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Geometer’s Sketchpad and GeoGebra
Dynamic geometry software includes programs such as Geometer’s Sketchpad and
GeoGebra where students can create figures and constructions easily. They can also adjust figures and move them once they are created and all the figure’s initial properties remain intact.
For example, a triangle with three equal sides can be created and then dragged so that it becomes larger but all the sides remain the same length. Survey data showed that out of 20 participants, six thought dynamic geometry software was beneficial to student learning and four believed it was the most beneficial technology. Also, only two said it was the technology they used most often. On the other hand, eight participants responded that they didn’t use any dynamic geometry software at all.
One of the teachers interviewed said he uses GeoGebra practically every other day. He mostly uses it as a presentation device and as stated earlier, he is able to make an animation on
GeoGebra, take a video screen capture of it, and then insert it into his PowerPoint slides. He feels like that makes a significant difference for student learning and often drives the geometry idea home for the students (Interviewee 6, personal communication, December 16, 2011). Another teacher has not used either Geometer’s Sketchpad or GeoGebra with her students but she has seen presentations for Geometer’s Sketchpad and she thinks it is amazing. She believes that it is so much more visual for the students and she feels that very few students would still not be able to understand concepts after working with it (Interviewee 3, personal communication, December
12, 2011).
One of the interviewees just started using GeoGebra with her students this year. She has put pictures from the ‘outside’ world into the program and had her students explore with figures and find geometry in the pictures. She has found that her ‘slowest’ kids are the ones that she Lolli 14 cannot slow down; they are excited about the program and want to race ahead of what she is showing. The students explore GeoGebra using a class set of laptops. She said she is planning to do a project in the 4th quarter where students create a ‘visual dictionary.’ The students will be creating and drawing pictures with software. She is going to use GeoGebra for her lower classes and TI-nspires for the upper classes (Interviewee 5, personal communication, December 15,
2011).
Another of the teachers interviewed was very passionate about using Geometer’s
Sketchpad. She said she uses it practically ever other day. She uses it more often as a demonstration and presentation device; the students have used it themselves four or five days throughout the year so far. Although not practical to be used for every geometry concept, she thinks it is good for the students and believes it definitely has more of an impact on learning than just presenting. For example, one of the activities the students did themselves a little while ago was about congruent triangles; the students were discovering which properties (i.e. SSS, SAS,
AAA) determined congruence and which did not. She said that just that day, a student referenced the activity that they had actually done four weeks ago. They are studying similarity now and he made the distinction that although equiangular does not lead to congruence, it does lead to similarity. This teacher has taken two classes on Sketchpad and she has a workbook from
Sketchpad with several worksheets for activities for the students. She believes that Geometer’s
Sketchpad is the most beneficial technology she uses (Interviewee 2, personal communication,
December 7, 2011).
One more teacher said she uses Geometer’s Sketchpad very rarely but she had just used it not too long ago to show triangle congruency as well. She thinks her students can now actually understand the concepts mainly because it is a better visual. Before, the students would just have Lolli 15 to take a new idea for granted (i.e. SSA is not a triangle congruency postulate). She could even draw a picture but that is not the same as Geometer’s sketchpad. With Geometer’s sketchpad, she definitely thinks the students get a better understanding. She uses it primarily for presentation
(Interviewee 4, personal communication, December 14, 2011). This same teacher told me how she uses Clickers extensively with her students. She says this is the #1 teaching tool in her classroom. She continued to say that it is so nice to show an example and then have each student try it at the same time. She claims that 100% of her students like using them and think they are fun (Interviewee 4, personal communication, December 14, 2011).
2. Miscellaneous Aspects of Technology Use
Technology Outside the Classroom
Teachers often provide resources for their students to learn while they are not in the classroom. These resources often involve technology. The survey asked teachers to identify which technologies, if any, they provide for student learning outside of their classrooms.
Seventeen replied that they use the school-wide website, 14 said they give extra website links or resources and 14 also said they provide a means for communication with their students.
One school uses a website called BrainHoney, and the teacher I interviewed said she takes advantage of it and that is where her students get all of their homework worksheets. She feels that her students definitely take advantage of it. She also likes it because she does not have to print out as much, especially for older students because all the juniors and seniors have laptops
(Interviewee 2, personal communication, December 7, 2011).
Another teacher said he recommends that his students check out videos on YouTube and
Kahn Academy if they need extra help or if they are just curious. He also posts notes and worksheets to Moodle, his school’s online website, and he gives them the link to their textbook Lolli 16 online, which also has extra worksheets. However, with all of these resources available to the students, he is pretty sure that neither the parents nor the students take proper advantage of it
(Interviewee 6, personal communication, December 16, 2011).
One of the interviewees said she gives her students website links about once a month, mostly as acceleration options. For example, she gave the students a website to further explore the Golden Ratio. She knows the next day that most likely only half of them looked at it and the other half did not, but that does not necessarily matter. She also finds critical thinking problems often and the students are encouraged to figure them out. She finds that they usually just search the Internet to find the answers. However, she has realized that this is not a bad thing because the students took maybe 20 to 30 minutes to look up the answer and consequently they end up finding other interesting websites about math that they bring in to share with the class
(Interviewee 3, personal communication, December 12, 2011).
Another school uses Progress Book to record and post students’ grades online as well as homework. The teacher I interviewed said she believes some of her students take advantage of it, but most of them hate it since their parents can automatically see their grades. She said Progress
Book even sends email notices of missing work or poor grades to parents at their request
(Interviewee 5, personal communication, December 15, 2011).
Another teacher I interviewed works at a school that also uses Moodle. She wasn’t completely sure how much the students take advantage of the website. She said that it is mostly an information post, and she believes it would be a lot better if the parents could access the website, but as of right now, only the students have access (Interviewee 1, personal communication, December 7, 2011). Lolli 17
The last teacher interviewed uses e-Campus, which is also her school-wide website. She posts videos, students occasionally take quizzes on the website, and the textbook is available online. She feels that probably less than half of her students take advantage of these extra resources (Interviewee 4, personal communication, December 14, 2011).
Availability of training and resources
The success of a new technology in the classroom is partly dependent on how much training and resources the teacher receives. The more comfortable and knowledgeable a teacher feels about a particular technology, the more they will use it with their students. Although the survey did not address this aspect of technology use, the interviews did.
Many of the teachers interviewed agreed that there was very little, if any, training provided with the introduction of new technologies. One teacher said that Geometer’s Sketchpad was available to her to use, but she uses it very rarely. She said there was no training for it, and not much help was given to learn how to use it (Interviewee 4, personal communication,
December 14, 2011).
Another teacher said that she has never used either Geometer’s Sketchpad or GeoGebra but that she would love to learn. She said that it was expensive; the school would first have to buy the program and then spend about $300 for each teacher to be properly trained. She said that the principal they have now would be willing to spend the money and there are other teachers that would like to have it, but making first steps to try something new is always a hurdle. Also, some of the teachers would probably not want to take 20 hours of their personal time to be trained on the program. However, if somebody would be willing to come to the school for an hour just a few times, it would be much easier to implement it. This same teacher uses an Elmo practically every day and she said there was not much training given for that. However, she said Lolli 18 her students are wonderful with the technology and are always very helpful to her. She also said that good collaboration with fellow teachers, especially the ‘tech wizards,’ is very helpful when getting a new technology (Interviewee 3, personal communication, December 12, 2011).
One teacher just started using GeoGebra and said that she was not given any training either, but she has gone to a few conferences and is planning on attending the T3 conference later this spring. However, she says she mostly has to explore it and try to learn it on her own
(Interviewee 5, personal communication, December 15, 2011). A different teacher took two classes on GeoGebra that she said were approximately $170 each. Fortunately, her school reimbursed her for the classes and she also finds time to play around with it a lot (Interviewee 2, personal communication, December 7, 2011).
Another teacher said her school does provide an initial training for new technology but after that, the teachers are on their own to learn how to use it. She said that she and the other teachers have to spend quite a bit of time playing around with the technology and collaborating with each other (Interviewee 1, personal communication, December 7, 2011). The last teacher interviewed said he did not get any training or resources to use technology, specifically referring to GeoGebra. However, he thinks that GeoGebra is pretty easy to use (Interviewee 6, personal communication, December 16, 2011).
Incorporating technology for Project-Based Learning
One teacher said that her school is striving to have more project-based learning. Thus, her students have done some projects already involving laptops and digital cameras. The projects have been centered on finding geometry in the real world. Most all of the work is done in-class because the school’s goal is for the students to learn the geometry standards by doing the project
(Interviewee 4, personal communication, December 14, 2011). Lolli 19
A different teacher said she uses Google SketchUp, which she described as ‘blueprint’ software. She has used it in the past for a service-learning project where her students have to design a building. She said the students were developing floor plans, practicing measurement skills, and exploring three-dimensions. She did the project for the duration of the second semester, which meant the students worked on it once every 2-3 weeks. Some students enjoyed it, but if they fell behind then they were complaining about it. Overall, she thought Google
SketchUp was a great software and made for a good project (Interviewee 1, personal communication, December 7, 2011).
3. Participants’ General Opinions on Technology
Negative responses
There were a few negative responses about technology from the survey and the interviews. The survey asked participants to list technologies that they use or have used that they believed have had negative effects on student learning. The following graph shows a summary of the survey results, which were just open responses.
Clearly, most participants said that none of the technologies that they use or have used have had negative effects. However, seven people said that they thought students easily get over- reliant on technology and might believe they cannot solve a problem without the technology. Lolli 20
Four of these seven participants said that the students become over-reliant on calculators specifically. Also, two teachers said that some of the technology they have incorporated has made particular concepts too easy for the students or has caused the students to not understand the full reality of why things are the way they are.
Only one of the teachers interviewed shared some negative views on technology. This teacher’s school has issued every junior and senior an iPad. They started providing tablets for juniors and seniors in 2003. However, the tablets have gotten more expensive so the students have iPads this year. She has mixed feelings about the iPads and tablets. She feels that they are a big distraction for a lot of students. Last year she taught Algebra II and she felt the computers were more of a distraction for her students; since she has a class set of laptops, there is no need for the students to have an additional computer. This year, however, she is teaching calculus and geometry classes. The students in the geometry classes are freshmen and sophomores so they do not have the iPads and the Calculus students are more advanced students and have not been distracted as easily by them. Also, the iPads do not have Flash player so a lot of the games are not supported which is definitely helpful in lowering distraction (Interviewee 2, personal communication, December 7, 2011).
Positive Responses
The survey also asked participants to list any and all technologies they use or have used that they believe have had positive influences on student learning. The following shows the distribution of the responses. Lolli 21
This graph clearly shows the top three technologies that teachers find to be the most beneficial to be SMART boards, Calculators, and Geometer’s Sketchpad or GeoGebra. One participant responded saying, “I think activities in Geometer's Sketchpad force students to think and conjecture on their own, more so than just a classroom discussion. I also think the models help students visualize how geometric objects behave while retaining specific properties. It helps kids that have a hard time picturing shapes get a good mental picture that they can refer back to.”
Another response said, “Geogebra, in particular, is dynamic so it allows students to visually see how different variable changes affect a geometric figure or transformation.”
The responses saying calculators were the most beneficial were mostly about the TI- nspires; one response was, “Ti-nspire activities and drawings on the calculator [help students] see how things are made and move” while another said, “The TI-nspire is an interactive tool to learn Geometry. This is the first calculator I've seen where you can do Geometric constructions or simply draw geometric figures.”
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Finally, the SMART board had several positive responses:
• “SMART software allows students to see pictures and do more with the pictures than a chalkboard allows” • “The SMART board allows me to prepare detailed diagrams in advance.” • “SMART board [enables the student] to draw and manipulate shapes in such a way that they can clearly see what is happening.” • “The interactive features of the SMART board have saved time and allowed for deeper understanding of concepts” • “Using the SMART board to highlight certain features of geometric figures and the ability to show a 3-dimensional shape as opposed to drawing it, helps the students visualize the concept better.” • “SMART Board gives students an interactive way to participate in class. It also allows them to SEE geometry more clearly.” A similar question was near the end of the survey; participants were asked to pick just one technology that they believed was the MOST beneficial to student learning. This pie chart shows the responses gathered.
It is easy to see that the distribution is very similar to the above responses. The top three choices again are SMART boards, calculators, and dynamic geometry software.
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Technologies to use more often
The following graphic shows the survey results for the question asking participants if they wished they could use any technology more often in their classroom.
Only two teachers said none, the rest were, for the most part, evenly dispersed across iPads, SMART boards, web-based activities, and Clickers. Four teachers said they wished they could incorporate the TI-nspires more often and seven would like to incorporate GeoGebra and/or Geometer’s Sketchpad. One response said, “Both [TI-nspires and GeoGebra] provide more opportunities for self discovery and individualized learning.” Another stated, “TI-Nspires and Geogebra, [because the students] are able to connect multiple perspectives together better than the older technologies.”
Asking this question during the interviews resulted in a wide range of responses. One teacher said she is interested to learn about response systems (Clickers). She thinks there is an application on the students’ iPads that may be similar to Clickers called the “Good Question
Program.” It has past AP test questions as well as other multiple-choice questions. She believes a Lolli 24 response system would be very helpful; without technology, teachers can still do a “voting” question, but if one ‘smart’ student raises his hand, then the seven people behind him raise their hand too even if they do not understand why that is the correct answer. The response system would eliminate some of those inaccurate responses (Interviewee 2, personal communication,
December 7, 2011).
Another teacher wishes he could have more computer lab time with his students so they could explore GeoGebra more. The students had just been able to explore GeoGebra for the first time in the computer lab the day of the interview. He gave them an introduction to build several different objects and then email him a copy of their final product. He would also like a class set of TI calculators, no matter what kind they are (Interviewee 6, personal communication,
December 16, 2011).
One school is looking into getting class sets of iPads. The teacher there is hoping there are some good applications for the iPads, perhaps from textbook companies that have to do with geometry. According to this teacher, GeoGebra announced a year ago that they are working on coming up with an iPad application soon. She would also like to incorporate the TI-nspire calculators more, but she feels that she needs to lead a discussion with the students and they need to learn the topic before they can do an exploration with the calculator (Interviewee 5, personal communication, December 15, 2011).
Another teacher says she cannot wait to use the TI-nspire Navigators, especially the immediate response system that the Navigators enable. Without the immediate response system, a teacher can ask her class a question from the day before and usually one student will pipe up.
However, the teacher easily ends up evaluating the whole class’ understanding on that one answer which is definitely not accurate. She also would love to work with the students on Excel Lolli 25 spreadsheets; students do not realize the mathematical power of Excel; most think it is just a word document and they put words in the boxes. If they could just understand how to do simple operations on Excel, such as add up a list of numbers or balance a budget, it would be very helpful for them (Interviewee 1, personal communication, December 7, 2011).
Differences in student learning because of technology
Teachers who agreed to take the survey were asked to answer three similar questions.
The first asked how they think their students would perform if they did not use the technology they do. The second question asked if the participants believed that the technology they use in their classrooms had an overall beneficial effect on student learning. And last, the survey asked the teachers if any of the technologies were necessary for student learning in geometry.
First question: 71% of participants thought that their students would do worse if they did not incorporate the technology they did and the other 29% thought their students would perform about the same; none thought the students would do better without technology.
Second question: The participants were practically unanimous in the answer to this question. Twenty out of 21 responses believed the technology they use has an overall positive effect on student learning while one said he or she had no idea. Again, none of the participants believed that the technology did not have a beneficial effect.
Third question: These responses are represented in the following bar graph. Lolli 26
The majority of teachers agreed that no technology was necessary for the students to learn geometry. Three teachers thought SMART boards were necessary and three more teachers thought calculators were necessary. Two participants said that some way of drawing geometry was necessary; one said, “A compass and protractor are necessary” and another simply replied,
“Something that will show drawing of concepts in geometry.”
During the interviews, more specific questions were asked. For example, if teachers had commented on the fact that they use a SMART board often, they were asked a question such as:
“Have you always had a SMART board since you have been teaching? If not, can you remember any specific lesson you have taught without the technology and now teach with it? Have you noticed any differences in student learning?” The technology inquired about depended on which one the teacher spoke most passionately about and which one they said they use the most often.
One teacher said she used Geometer’s Sketchpad practically every other day. She has been teaching for six years and only the first year she did not use Geometer’s Sketchpad. When asked the above question, she replied that she could definitely see better results between lessons from her first year and lessons now. However, the year she did not use Geometer’s Sketchpad, she was a first-year teacher, so she feels that she is a better teacher now. Understandably, it is Lolli 27 hard for her to separate results from teaching experience and technology effects (Interviewee 2, personal communication, December 7, 2011).
A different teacher uses an Elmo on a daily basis and thinks it is much better for the students than a white board or chalkboard. She has taught for a while and has used the Elmo for the past four to five years. She believes it really helps their thinking processes. She has used it for about four years now. It is better because she can face the students while working instead of having her back towards them. The Elmo is colorful, has graphics and graph paper, and has the ability to easily pull up websites. It is just more visual for the students and accessible. She still has three white boards around her room but she hardly ever uses them. Every now and then she has the students put up proofs on the white boards all over the room. But if the power goes out or some other technical difficulty arises and she has to use the white board again, all her students complain because they like the Elmo so much (Interviewee 3, personal communication,
December 12, 2011).
A teacher that has recently started using GeoGebra said it was hard to really differentiate between past and present lessons. She says this is because she uses GeoGebra as an extra exploration and uses it to build on top of things she has already discussed. She does believe her students are making connections better because of GeoGebra and she has realized that they do not have the ‘confused face’ for as long. She has found that they are also more active and engaged in class (Interviewee 5, personal communication, December 15, 2011).
One teacher I interviewed is extremely passionate about using Clickers with her students.
She has been teaching geometry for eight years and the first four years she did not have the
Clickers. She can tell that the students are definitely more engaged. However, she feels she cannot really comment on whether student performance has improved because at the beginning Lolli 28 she was teaching sophomore geometry and now she is teaching freshman geometry, which results in more motivated students. But all the students definitely like using them and they are more engaged overall (Interviewee 4, personal communication, December 14, 2011).
Conclusions
The object of this study was to collect and organize high school geometry teachers’ viewpoints on technology use in their classroom. It was mainly to see if they believe any technologies they use have beneficial effects on student learning. This study started with the goal of answering two questions: one, do certain technologies enhance student learning in geometry and two, are these technologies essential to teaching and learning geometry?
The first question of whether certain technologies enhance student learning in geometry was clearly answered by the teachers who completed the survey and who were interviewed. As previously discussed, the participants believe that SMART boards, GeoGebra, Geometer’s
Sketchpad and TI-nspire calculators all have beneficial effects on student learning. This study has revealed that, for the most part, teachers do not believe that calculators other than the TI- nspires enhance student learning in geometry. Also, any teacher that uses a SMART board or
Geometer’s Sketchpad or GeoGebra had no negative things to say about it; some teachers wished they could use these more, and others just raved about them and how they were great visuals for students and how easy it is for students to interact with them.
The survey and interview data from this study does not answer the second question as clearly. Are the technologies that teachers find to enhance student learning essential to learning geometry? Practically all of the survey participants and 100% of the interviewees agreed that the technologies they use are beneficial to student learning. However, the responses were almost opposite when it came to whether those same technologies are necessary. The large majority of Lolli 29 teachers responded that the technologies are helpful but not necessary. It is interesting to note that SMART boards and graphing calculators were said by a few teachers to be necessary but neither GeoGebra nor Geometer’s Sketchpad were said to be necessary even though they were listed along with SMART boards and graphing calculators to be the most beneficial for student learning. Thus, although the study found several technologies to be beneficial to student learning, according to the teachers surveyed and interviewed, it does not seem that any of these technologies are necessarily essential to geometry learning.
There were several other interesting ideas that emerged during the course of this study. A common theme throughout was the fact that there does not seem to be enough training when it comes to new technologies in the classroom. However, this study does not, by any means, prove that schools are not doing enough to provide the necessary training for new technology. Instead, it draws attention to the fact that resources and training are very beneficial to teachers trying to learn how to use and implement new technologies in their classrooms. All the teachers that had to teach themselves seem to be doing fine with their technologies now, but perhaps if they had more training at the beginning, it would have been easier to learn and they might be more experienced with it now.
A very similar topic that came up a few times in the interviews was that some of the teachers would need more resources to better incorporate technology for their students. For example, many of the teachers that currently use GeoGebra or Geometer’s Sketchpad said they use it most often as a presentation device and the students do not get to use it themselves very often. Granted, some teachers had access to a cart of laptops so the students could use it more often. However, there were also some teachers that did not have access to a cart of laptops or a computer lab, so it is difficult for them to allow the students to explore with these technologies. Lolli 30
Although this study mainly found positive opinions and views of technology, there were a few negative views. These show that although technology in the classroom seems to be phenomenal and is seemingly improving students’ geometry learning, there are still precautions when it comes to technology, especially over-use. This study did not find any opinions of technology hurting student learning in geometry, but there were quite a few responses recognizing that over-use of technology in general is not good for the students. It can lead to students believing that they cannot solve a problem without a particular technology, or the students may not understand the full reality of a problem because the technology could make it too easy to see the final result instead of all the intermediate steps. Calculators were the major technology brought up during the study that are helpful for the students but can also hurt them because of over-use. A possible compromise could be that some new concepts would be introduced ‘by hand’ and once the students have a decent understanding, the technology could be introduced for further exploration.
Another topic that came up during the course of this study was that the teachers have mixed views on technology used to benefit student learning outside the classroom. Every teacher interviewed uses some form of technology for “outside the classroom” learning. However, about half thought the students did take advantage of it and half thought they did not. It seems to be a necessity to provide students with technology support for outside the classroom time, but it will do no good if the students are not taking advantage of it. This may be a topic worth looking into in the future: to understand how and why those students that do take advantage of the material do so and then see if those findings can be applied to other schools.
At the beginning of this write-up, a few research studies were quoted. One by Holden and
Hannafin said that teachers’ motivations for using technology are almost always based on their Lolli 31 personal feelings towards it. I think this study partly addresses this statement. The survey and interview data seem to suggest that teacher use of technology is not only based on their feelings about it but how the students will benefit from it. The range of answers and reasons given to the survey question, “what technologies did they wish they could use more often,” show that the teachers want to use technologies based on how beneficial they seem to be on student learning.
However, it also came across in the interviews that some teachers did use technologies more often than others based on how well they understood and liked the technology. Thus, this study seems to show that Holden’s and Hannafin’s statement is partly true but also partly false since the teachers do seem to base use of technology on how beneficial it is to the students.
Holden also stated that teachers are neutral on whether technology affects in-class activities. I believe this study shows that statement is inaccurate. All of the interviewees and practically all of the survey responses showed that teachers definitely think the technologies they use positively affect in-class learning. The teachers agreed that engagement improves with technology use and the students are excited to use the technologies themselves. The only thing that is still neutral according to the participants in this study is whether technology actually enhances student learning and performance on assessments.
Another researcher, Dye, said that often students have difficulties learning how to use new technology and that the teachers sometimes spend more time giving a technology lesson instead of a geometry lesson. However, this survey actually found the opposite; teachers are the ones that need the extra training, but it seems that the students pick up on it very easily and the interviewees said that they were very willing to help out if technical difficulties arose.
Finally, the research done by Stols and Kriek had said that further investigations should focus on how and for what purpose teachers used dynamic geometry software in their Lolli 32 classrooms. This study showed that most of the time, teachers are using dynamic geometry software as a means of presentation, but as often as they can, they have the students do explorations with it on laptops or in a computer lab.
As already stated, this study cannot make definitive statements or generalizations as to which technologies enhance learning or which should be implemented in all geometry classrooms. This is because of the limited number of participants and the fact that the data was collected solely through surveys and personal interviews and not statistical, experimental or observational data. However, this study has provided several starting points on which to base further research. First, it has pointed to three main technologies that teachers seem to find beneficial to student learning in geometry: SMART boards, TI-nspires and GeoGebra and/or
Geometer’s Sketchpad. The effects and possible benefits of these three technologies should be further explored. Also, there were common statements among the participants, both in the interviews and surveys, regarding the effects of good technologies. First, a beneficial technology enables the students to make connections more quickly and easily. Second, technologies provide an interactive way for the students to become involved in their learning, manipulate geometric objects and figures themselves, and to even teach their peers. Third, a beneficial technology is one that can give the students a better or extra visual of the material. Some of the teachers believe that if the material is visually represented, there is a better chance that the students will understand it.
A few aspects of this study are discussed here and the possible impact of these aspects on the validity of the data and opinions collected.
First, this study was restricted to schools in Franklin County and was at the mercy of whichever schools responded to the initial email requesting contact information. This study went Lolli 33 through a few stages, each one lessening the number of possible results. The first stage was contacting the 60 high schools in Franklin County and seeing how many schools responded, which turned out to be about 30%. The second stage was emailing the 38 teachers individually from the list compiled from stage one responses. Sixty-three percent of these teachers responded, willing to participate. Of those, 92% actually took the survey. As already discussed, six interviews were completed. Thus, out of 60 schools contacted, 10% resulted in personal interviews. Although this sample clearly does not give a true representation of the teachers and high schools in Franklin County, the return rate was actually impressive; it was exciting to receive this many responses, and thus a variety of data and opinions.
A second aspect to consider is the types of schools represented by the participants. More than half of the participants represented suburban public schools while those representing parochial schools made up a quarter of the participants. Thus, charter, urban public, and private schools were poorly represented. At the beginning of this study, it was decided that the types of schools would not matter, because the teachers’ viewpoints on technology (what they use presently, what they have used in the past and what they have heard about) was the only concern and would not be affected by what school they are teaching at. However, now at the conclusion of the study, it is apparent that certain types of schools and their available resources may have had an impact on whether a teacher or the school itself was willing to participate. A school that may not have enough resources to provide the newest, up-to-date technologies to its teachers, may have felt that there was no point in taking a survey that is centered on technology. Of course, there is no way to determine whether this is the case or not, but it is something to consider. Lolli 34
A third aspect of this study to consider is whether gender of the participants matter.
Eighteen of the 24 surveys sent out went to female teachers and five of the six interviews were with conducted with females. Gender does not seem like it should make any difference when it comes to opinions on what technology is most beneficial to student learning. However, the possible impact of gender of teachers and types of schools represented should be examined for future studies.
The major unanswered question left by this study is the extent to which the technologies discussed positively enhance student learning. To determine this, more data collection would be needed than simple interviews or surveys. Perhaps, experiments could be conducted. For example, two classes would be taught the same geometry lesson but one would be taught with a particular technology and one would be taught without it. Some things to consider would be whether the same teacher would teach both classes or not, how enhancement of student learning would be judged, and how much training would be given to the teacher(s) ahead of time.
In conclusion, although this study cannot make broad claims about technology, it has shown which technologies several teachers in central Ohio believe to be beneficial to student learning in geometry, as well as commentary and discussion on other issues regarding technology use in geometry classrooms. These technologies and issues should be explored further in future studies so broad claims can be made and eventually plans can be put in motion to provide every geometry classroom the most beneficial technology for student learning.
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References
Ball, D. (2002). Teaching and learning geometry using dynamic geometry software. Micromath,
18(3), 46-48. Available from: Education Full Text. Accessed August 5, 2011.
Driscoll, D. L., & Brizee, A. (2010, April 17). Conducting Primary Research. Retrieved from
http://owl.english.purdue.edu/owl/resource/559/1/
Dye, B. (2001). The impact of dynamic geometry software on learning. Teaching Mathematics &
its Applications, 20(4), 157-169. Retrieved from EBSCOhost.
“Franklin County Community (Charter) Schools.” (2011). NMP Consulting. Retrieved from
http://charter.kitoba.com/schools-county-Franklin.html.
“Franklin County Private High Schools.” (2011). Private School Review. Retrieved from
http://www.privateschoolreview.com/county_high_schools/stateid/OH/county/39049.
Funkhouser, C. (2002). The effects of computer-augmented geometry instruction on student
performance and attitudes. Journal of Research on Technology in Education, 35(2), 163.
Retrieved from EBSCOhost.
Grunwald and Associates. (2010). Educators, technology and 21st century skills: Dispelling five
myths. Retrieved from Walden University, Richard W. Riley College of Education
website: from www.WaldenU.edu/fivemyths
Hannafin, R. D. (2001). Learning with dynamic geometry programs: Perspectives of teachers and
learners. Journal of Educational Research, 94(3), 132. Retrieved from EBSCOhost.
“High Schools in Franklin County, Ohio” (2011). Find Schools in Ohio – School Tree. Retrieved
from http://ohio.schooltree.org/high/Franklin-County-Schools.html. Lolli 36
Holden, H., Ozock, A., Rada, R. (2008). Technology use and acceptance in the classroom:
Results from an exploratory survey study among secondary education teachers in the
USA. Interactive Technology and Smart Education, 5(2), 113 – 134.
National Council of Teachers of Mathematics, Inc. (2000). Principles and standards for
mathematics. Reston, VA: NCTM, Inc.
Stols, G., & Kriek, J. (2011). Why don't all maths teachers use dynamic geometry software in
their classrooms?. Australasian Journal of Educational Technology, 27(1), 137-151.
Retrieved from EBSCOhost.
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Appendix A: High Schools Contacted in Franklin County
Arts & College Preparatory Academy (ACPA) Horizon Science Academy Columbus Beechcroft High School Independence High School Bexley High School Lincoln High School Bishop Hartley High School Linden-McKinley High School
Bishop Ready High School Marburn Academy Bishop Watterson High School Marion-Franklin High School Briggs High School Mifflin High School Brookhaven High School New Albany High School Canal Winchester High School Noble Academy – Columbus Centennial High School Northland High School The Charles School at Ohio Dominican University Ohio School for the Blind
Columbus Alternative High School Ohio School for the Deaf Columbus School for Girls Pschtecin Public School Columbus Torah Academy Reynoldsburg High School Dublin Coffman High School Scholarts Prep and Career Center for Children Dublin Scioto High School South High School East High School St. Charles Preparatory School Eastmoor Academy St. Francis De Sales High School
Excel Institute Summit Academy Transition School Focus on Collective Integrity Academy The Graham School Focus Learning Academy of Northern Columbus Thomas Worthington High School Focus Learning Academy of East Columbus Tree of Life Christian School Focus Learning Academy of SW Columbus Upper Arlington High School Gahanna Christian Academy Virtual Community School of Ohio Grandview Heights High School Walnut Ridge High School
Grove City High School West High School Groveport Madison High School Westerville-South High School Hamilton Township High School Whetstone High School Hilliard Darby High School Whitehall Yearling High School Hilliard Davidson High School World Harvest Christian Academy
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Appendix B: Survey Questions and Data
Consent Form: By clicking the arrow button below, you agree to the following:
You are being asked to participate in this research project that seeks to investigate teachers’ views of technology in the classroom and its possible effects on student learning. To determine this, participants are being asked to complete the following short survey. This is the only request that is being made of you.
There are no risks to you in taking this survey besides the fact that it may take you 15 minutes to complete. You will not be compensated in any way for filling out this survey.
Your name will never appear on any survey or research instruments. No identity will be disclosed in the data analysis or reports of the collected data. Collected data will only be available to the principle investigator. All materials will be destroyed at the completion of the research.
You are under no obligation to complete this survey and you have the right to withdraw from completing this survey at any time.
A copy of the final report of this study will be supplied to you at no cost, upon request.
If you have any further questions about your participation, you may call/email Melanie Lolli at (614) 557-6885 or [email protected].
Part I: Technologies you USE or HAVE USED in your classroom Q1: Do you use calculators with your students? Order Answer Responses Percent 1 Yes 21 95 2 No 1 5 Total 22 100%
Q2: If yes, what kind of calculator do you use? (i.e. standard, scientific, TI-83, TI-nspire) Order Answer Responses Percent 1 21 100 Scientific, like the one used on the OGT.
TI-82 or scientific
Ti-30XSII (as used on the OGT)
TI-83, TI-84, TI-Nspire, TI-Nspire CAS
Standard, scientific, TI-83+, TI-30 Lolli 39
TI-nspire
Scientific and/or TI-83
TI-84
Mainly scientific. Kids are free to use graphing calculators but we don't make much use of them as a required component.
Mostly TI 83,84
TI-83 Plus, TI-84 Plus, TI-Nspire, TI-Nspire Cas
TI-30XIIS
TI-83 and 84
Scientific and TI-84
TI-Inspire
Scientific
Mainly TI-30. Standard OGT calculator.
Scientific with Geometry students TI-83 or TI-84 with Calculus students
I currently use the TI N-Spire CX with my classes. I have also used the TI-83 and TI-84.
We use a scientific calculator as well as the TI-84 Plus Silver Edition
TI-83, TI-inspire
Total 21 100%
Q3: If you use calculators, do you use any software or other technology to support the calculators (i.e. overhead adapter, online websites specific to the calculator)? Order Answer Responses Percent 1 Yes 15 68 2 No 7 32 Total 22 100%
Q4: If yes, what is the supporting software? Order Answer Responses Percent 1 15 100 TI-SMART View
Overhead adapter, computer emulator software
Lolli 40
Projector w/ SMART board w/ TI
Smart Board
Ti-nspire Software
TI Graphing calculator software on projector/SMART board
TV adapter
TI-connect
Overhead Adapter, TI-Nspire Emulator Software, TI-education website
Overhead adapter
SMART board/notebook ... I use the TI emulator
Teacher software for Inspire
Just got a Navigator
Overhead adapter
A computer version of the calculator that can be projected on the SMART board
TI Navigator (for wireless connection of calculators in the classroom); N-Spire files from websites
I use the TI Presenter that runs through my SMART board.
Total 15 100%
Q5: Do you use technology for presentation or lecture? (Please check all that apply) Order Answer Responses Percent 1 SMART board 19 33 2 Overhead projector 17 29 3 A digital projector connected to your computer 14 24 4 Document Camera "Elmo" 5 9 5 Other 3 5 6 None 0 0 Total 58 100%
Q6: Do you use internet resources to support lessons or activities? (Please check all that apply) Order Answer Responses Percent 1 Interactive websites 11 26 2 Review games/quizzes/practice websites 12 29 Lolli 41
3 Videos, podcasts, etc 9 21 4 Other 5 12 5 None 5 12 Total 42 100%
Q7: Do you utilize any of the below software in your classroom? (Please check all that apply) Order Answer Responses Percent 1 Geometer’s Sketchpad 10 42 2 Geogebra 4 17 3 Cinderella 0 0 4 Other 2 8 5 None 8 33 Total 24 100%
Q8: Do you use any of these other miscellaneous technologies in your classroom? (Please check all that apply) Order Answer Responses Percent 1 Laptops 9 29 2 Classroom Response Systems “Clickers” 4 13 3 Miscellaneous SMART accessories 6 19 4 Other 2 6 5 None 10 32 Total 31 100%
Q9: Do you use or make available any technology to benefit your students outside the classroom? (Please check all that apply) Order Answer Responses Percent 1 Personal website 3 6 2 School website 17 33 3 Websites or software for remediation, enrichment, etc 14 27 4 A way to communicate with students (i.e. email, discussion boards) 14 27 5 Other 3 6 6 None 0 0 Total 51 100%
Q10: Please list any and all other technologies you use or have used as a geometry teacher: Order Answer Responses Percent 1 10 100 Video lessons supplied by textbook company
We have a class website as well as an online grade book.
iPads, Flip Cameras, Digital Cameras
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Geometer's Sketchpad (about 4 years ago)
You have already mentioned all the technology that I use in my classroom.
I use interactive material from OhioRC and Illuminations quite often.
SketchUp
I have a class text account.
I use Geometer's Sketchpad extensively, both as a presentation tool and for students to use in pairs to complete activities and explorations. I have a school-supported website (BrainHoney) that I use to post worksheets, homework, links to other material and to communicate with students. I also use scientific calculators with Geometry students.
We also use google docs as a way to share information. Students complete projects throughout the year and we use google docs to share, provide feedback and grade student work.
Total 10 100%
Part II: Effect of Technology on Student Learning
STUDENT LEARNING in the course of this survey refers to performance on in-class assessments, engagement in class, ability to recall information, ability to apply concepts/ideas to homework exercises and/or in-class activities, and overall interest in geometry.
Q11: What technologies that you listed on the previous pages, if any, have you observed to have BENEFICIAL effects on student learning? Why? Order Answer Responses Percent 1 20 100 SMART software because it allows students to see pictures and do more with the pictures than a chalkboard allows.
Videos let students see changes to geometric figures. The SMART board allows me to prepare detailed diagrams in advance. Calculators allow for more accurate calculations
Calculators to speed up and verify calculations.
The TI-83, TI-84, TI-Npsire, TI-Nspire CAS, and Geogebra are all beneficial in that they when use appropriately they help students make connections.
Ti-nspire activities and drawings on the calculator to see how things are made and move
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SMART Board--ability to draw and manipulate shapes in such a way that they can clearly see what is happening.
Senteo Clickers--the #1 piece of technology I use in my classroom. We use them 4-5 days a week--provides immediate feedback for me and the students themselves.
The interactive features of the SMART board have saved time and allowed for deeper understanding of concepts
Websites that have animations on them, especially in geometry, regarding shapes that can be dynamically changed. Geometer's sketchpad is also very good with the dynamic aspect as well.
Using geogebra, powerpoint animations help visually show relationships in transformations. Geogebra, in particular, is dynamic so it allows students to visually see how different variable changes affect a geometric figure or transformation.
TI-83 Plus, TI-84 Plus, TI-Nspire, and Geogebra have all been beneficial in various ways.
When doing activities and lessons using these students tend to be more actively engaged, develop more self-learning strategies, and can often get to the generalizations, postulates, and theorems much more quickly than without the technology. The newer TI-Nspire and GeoGebra tools are now allowing more students to develop, see, and use more interactions between the Algebra and Geometry skills.
The students love to work at the Elmo. They come up and explain problems to the class and all seem to benefit from it.
Interactive tools that allow students to see what is happening. If they see it happening they remember it more.
Using the SMART board to highlight certain features of geometric figure and the ability to show a 3 dimensional shape as opposed to drawing it help the students visualize the concept better.
Smart Board - gives students an interactive way to participate in class. It also allows them to SEE geometry more clearly.
TI Inspire - great tool. Again, the Inspire is an interactive tool to learn Geometry. This is the first calculator I've seen where you can do Geometric constructions or simply draw geometric figures.
The texting as reminders for my students.
The Senteo response system has been hugely beneficial strictly for the immediate feedback it gives. This is not necessarily geometry specific though.
I think activities in Geometer's Sketchpad force students to think and conjecture on their own, more so than just a classroom discussion. I also think the models help students visualize how Lolli 44
geometric objects behave while retaining specific properties. It helps kids that have a hard time picturing shapes get a good mental picture that they can refer back to.
The TI N-Spire is allowing exploration easily in the hands of students. Therefore students can gain understanding in why/how concepts form.
We use Google docs to keep track of all of the Theorems and Postulates we learn throughout the year and students use the Google doc as a resource. I also have all of the notes and formative assessments posted on my website so that students can access them at home.
Websites with videos that demonstrate a specific skill are helpful for demonstration.
We also use ALEKS to supplement prerequisite skills and review of skills we've worked on in the class
SMART board to demonstrate a skill
Total 20 100%
Q12: What technologies that you listed on the previous pages, if any, have you observed to have NEGATIVE effects on student learning? Why? Order Answer Responses Percent 1 18 100 No negative effects
Also calculators. Sometimes students become too reliant on calculators and do not do simple arithmetic in their heads.
The negatives are the often the students become overly reliant on the technology and don't think they can do a problem without it.
None
None
Misuse (or overuse) of calculators lead to bad habits and poor comprehension of basic skills
Students tend to use calculators too much at times for simple math.
I think technology is neither necessarily good nor bad. In general, I don't believe I have allowed technology to have negative affects of student learning. If so, it has been in the form of me spending too much time on a PowerPoint when I could be thinking of a better explanation. Or subconsciously giving the impression to students that it is the teacher's job to entertain with technology.
In general for all of them, at times students become overly Lolli 45
dependent on technology and assume that it is the only way they can do something.
None
Sometimes the applications on the Geometer's Sketchpad happen so "easily" that the students don't experience the hands on reality of why things are the way they are.
I sometimes think it is helpful for the student to draw a shape on their own in order to learn the different parts of a figure.
Inspires cost a lot but that is not negative toward learning just toward access.
None.
I think the school website can be a very good resource for students. I also think it can be a crutch at times because students are not responsible for writing down their homework assignments. Also, sometimes calculators can be viewed in the same way. At my high school, however, Algebra 1 students cannot use calculators, and so I do not notice this as much because students got used to not having them the year before.
None
None
Some videos are good for demonstration. Since they are not captioned, it is impossible for the students to fully understand the concepts. It tends to take more time than me showing and explaining at the same time.
Total 18 100%
Q13: Have you found any of the technologies on the previous pages to be difficult for students to use or understand? Order Answer Responses Percent 1 20 100 The airliner that goes with the smart software is hard for students to write on. So if I want to see a student work out a problem then I either send them to the chalkboard or they write on a whiteboard.
No
No
If the students are expected to learn how to use them on their own it is very difficult for them, but if given guidance on how to do something they are usually ok.
Yes, the new TI-nspire calculator Lolli 46
GeoSketchpad is difficult for them at first--they typically pick up on it quickly.
No
Some of the Sketchpad activities are hard for the kids to follow if we take them to the computer lab to do. Certainly the first few times there is a learning curve.
None
Most technologies students have difficulty using at first. Even the compass and protractor (if you call that technology).
All of them require time to teach the students how to use them and are difficult for the students to use without some guidance.
No, the students are much quicker at catching on than we adults.
Our computers do not support some of the interactive tools that we have.
No...They know more than me!
I believe there is a learning curve (especially for adults) to learning to use the Inspire. After you 'get it', the possibilities are endless!
None
Not really. Students in general are quick to pick up new technologies.
Everything new takes a little getting used to, but no, students seem to pick up on new technology quickly.
No
Websites that are not captioned
Total 20 100%
Q14: Which of the listed technologies, if any, do you feel you use most often in your classroom? Order Answer Responses Percent 1 20 100 The SMART software with projector is used most everyday in my class.
SMART board
TI-83/TI-84s and the computer with projector.
TI-nspire calculator
Lolli 47
SMART Board (daily), Senteo Clickers (daily)
SMART Board
Animations and applets. Sketchpad once in a while. Scientific calculators when needed.
Website for the text book
PowerPoint, Geogebra, Internet Searches, Email, Moodle
TI-83 Plus, TI-84 Plus, and TI-Nspires
Daily - calculators, Elmo and the overhead.
I use the SMART board on a daily basis. However, there are times that it acts more as a glorified overhead, not as an interactive tool.
The SMART board
SMART board
Overhead
SMART board and Senteo clickers.
Sketchpad
TI N-Spire; SMART board
SMART board, website and Google docs - we are just now starting to use a document camera and I am finding it very helpful.
SMART board and ALEKS.
Total 20 100%
Q15: Part II continued: Effect of Technology on Student Learning Approximately how often do you incorporate technology into your geometry lessons (such that the technology is part of the lesson; NOT to take attendance or record grades, for example)? Order Answer Responses Percent 1 Hardly ever 0 0 2 2-6 times a year 0 0 3 Once or twice a month 3 14 4 Once or twice a week 5 24 5 Every day 13 62 Total 21 100%
Q16: Are there any technologies that you wish you could incorporate more often? If so, why? Order Answer Responses Percent Lolli 48
1 18 100 I would like to use the SMART clicker response more.
I just went to a short presentation on Geogebra and would like to get more info on it so that I can begin using it in the future.
Web based activities, practice problems and assessments.
TI-Nspires and Geogebra, they are able to connect multiple perspectives together better than the older technologies.
iPads...very hands on, students are interested and engaged--allows for individual work, as well as group work. Apps to demonstrate concepts.
No
I use the SMART board most every day. I'd like to find more videos to incorporate. That's the next big challenge.
I wish I had more time and access to computer labs to use Geogebra as a class.
TI-Nspires and GeoGebra: Both provide more opportunities for self-discovery and individualized learning.
No
I would like to learn more about geometer's sketchpad and Geogebra
I'm just learning to use the Navigator so I will be incorporating it more soon!
SMART board
Geometer sketchpad. Especially when dealing with classifying shapes, I have seen this program to be hugely beneficial in terms of getting to 'play around' with the shapes, making observations, and then reaching conclusions.
I am interested in using clickers, but have not pursued that yet.
I'm still learning ways to use the N-Spire.
I would like to use geometry sketchpad
More websites to encourage more independent learning
Total 18 100%
Q17: Are there any technologies that you believe are used too often in your classroom? If so, why? Order Answer Responses Percent Lolli 49
1 16 100 No
No
No
No
No
No.
Student's cell phones. Why? Because they are not supposed to be used w/o teacher permission.
SMART board, computer, and projector. Many times due to time constraints I must use a more lecture-based approach to lessons.
No
No
No
None
No
No
No
No
Total 16 100%
Q18: How do you believe your students would perform if you did not incorporate the technology that you do? Order Answer Responses Percent 1 Worse 15 71 2 The same 6 29 3 Better 0 0 Total 21 100%
Q19: Do you think that the technology you use in your geometry classroom has an overall beneficial effect on your students’ learning? Order Answer Responses Percent 1 Yes 20 95 2 No 0 0 3 I have no idea 1 5 Lolli 50
Total 21 100%
Q20: Please explain your answer to the above question: Order Answer Responses Percent 1 19 100 We are able to do more and see more application to the topics the students are learning.
Technology allows students in geometry to see two- and three- dimensional figures more clearly. Many students have trouble visualizing shapes, so the technology can be helpful. It also helps them grasp some difficult concepts (like the location of the incenter, circumcenter, centroid, and orthocenter). The use of calculators is also beneficial to all math students. Students may understand a geometry concept, but a simple arithmetic mistake can cause an incorrect solution. A calculator helps!
Presenting material in a variety of ways is helpful to all students. Technology also allows me to reach students with different learning styles.
The technology helps the students to make connections, which in turn deepens their understanding of various topics.
I think it enhances their learning. I still think they would understand it without but I think it makes them see things easier.
Technology is engaging to students and really allows geometry to come to life for them.
The ease at which material is accessible allows for more quality processing and learning time
For example, to be able to grab two similar triangles and change their size but still show the ratio stays the same. That's powerful. Anything dynamic is a huge visual piece that helps understanding.
They are able to make many concepts more concrete and have more opportunities for self directed learning.
The technology of graph paper, compasses, protractors, colors of markers, etc. help to perk the students' interest and keep them on track for a longer period of the class.
The technology allows me to displays geometric concepts more accurately, which allows learning to be more fluid.
I think today's kids are just used to the technology and often expect to see it in the classroom. At my school the same subject teachers try to give the same assessments in order to collect data. Some of the teachers on my team have access to SMART boards and others do not. The overall test results seem to be the relatively the same. Lolli 51
I believe technology benefits the students because they can experience their learning of Geometry in more than one way. They need to see, hear, write, touch, explore, etc. to understand Geometry more clearly. Technology allows the teacher to help students experience Geometry in a wider variety of ways.
I just think that anything that adds to my lessons is beneficial.
Certain applets or gizmos allow for animations that cannot be performed with more traditional teaching tools. These allow students to make deeper connections by actually seeing and internalizing these more abstract concepts being acted out.
I think there are many ways to be a good teacher. You don't need to be a technological wizard to be a good teacher. At the same time, I do think technology can add to lessons and inspire students to think more deeply about mathematical concepts. I often think some of the resources I share with my students spark an interesting question or comment.
The more exploration students do to learn concepts, the better they will understand and apply the concepts.
I think technology has allowed students to access the curriculum on their own time and where they want to since it is all located online. I also use an online text that offers many interactive options.
I think technology provides another tool to help students learn. The students like technology so they are more likely to work on a skill if it is used.
Total 19 100%
Q21: Can you pick ONE technology listed previously that you believe to be the most beneficial to student learning? Order Answer Responses Percent 1 19 100 SMART technology
SMART board
Web-based material
TI-Nspire
Geometry drawing..
Senteo clickers
SMART board
Dynamic animations and applets. Lolli 52
Video projector with computer.
Elmo
The SMART board in general.
Calculators
Graphing Calculator
Calculators
Geometer sketchpad - this allows students to get their hands on the content. This is almost always more powerful than any presentation that can be given to them.
Sketchpad
SMART board
SMART board.
SMART board
Total 19 100%
Q22: Do you believe that using any of the technologies discussed above are a NECESSITY to students’ learning of geometry? If yes, which one(s)? Order Answer Responses Percent 1 19 100 I don't know that it is a necessity, though with the use of so much technology in the world it has become second nature for students.
Students can learn without the technology, so none are really a necessity
No
They are not a necessity, however they all assist in deepening the understanding and in most cases speeding up mastery of concepts.
Something that will show drawing of concepts in geometry...
No--but highly beneficial
No
No, not a necessity. But very helpful, yes.
A compass and protractor are necessary. A computer with a video projector is arguable, but I would say they are necessary.
Lolli 53
NECESSITY - none
No.
Yes. They have to have access to the trig functions. And many of our students still need them for basic calculations.
Graphing Calculator
Graphing Calculators
Smart board. I'm somewhat attached to it ;)
No
No, but they sure are helpful!
I believe that Geometry is very visual so the use of the SMART board becomes necessary in displaying the information.
Students can learn without technology. Technology just helps students understand skills better.
Total 19 100%
Lolli 54
Appendix C: Interview Questions
Do you use Dynamic Geometry Software in your classroom, and if so, what is it? Do you use this software more often for presentation or exploration?
Do you use Technology to benefit students outside the classroom? Do you think it is beneficial for the students? Do you think the students take advantage of what you provide?
Do you use calculators with your students, and if so, which kind? What is the primary use of the calculators?
Have you always used [specific technology] since you have been teaching? [If not:] Can you remember a lesson you taught when you did not use the [specific technology], and a lesson you have recently taught, using it? Were there any differences in the students’ learning?
For [specific technology], did you receive any training or resources to learn the best ways to use it or did you have to learn it on your own?
What technology do you wish you could incorporate more often? Why?
What technology do you find to be the most beneficial for student learning? Why?
Any other technologies that you use or have heard of that you would like to discuss?
Miscellaneous questions from survey data: What is SketchUp? (A Google app?) What is a “class text account”? What is the TI-emulator? What is ALEKS? Do you have any experience with it?