ETEC 533 – Technology in the Mathematics and Science Classroom
Hello everyone! I am doing option 1 (a blog) for assignment 2. I have done all my posts for the efolio as listed in the lessons.
Although, I am not sure if there is a synthesis required in the end. If so, what should it include? I have tried to get in touch with Christopher recently but he seems to be very busy with the finals and hasn’t gotten back to me.
Could someone please clear this up?
Thank you,
GK
Hello everyone!
I came across this simulation online that you can use to show 3D rotation of objects in your math class when introducing surface and volume unit to grade 8/9 students.
http://cdac.olabs.edu.in/?sub=80&brch=20&sim=161&cnt=4
In addition to simulation, it also talks about theory, procedure, and animation. Check it out!
An excerpt from Srinivasan et. al. article on Reality versus Simulation is a perfect example of the importance of information visualization for mathematics. One of the participants in the study discussed in Srinivasan et. al’s article states, “…when you’re getting the signals on the computer all you’re doing is typing the equation and getting a graphic, but when you’re getting it on the lab equipment, you’re actually setting frequencies and … it seems more real” (Srinivasan et. al., 2006, p. 139). Every teacher tries to do his/ her best to be able to help students understand the learning outcomes of a lesson and it becomes even more rewarding for a teacher when a child is able to visualize the learning and see it as something “real”. Information visualization helps teachers across the globe achieve that reward of helping students see textbook problems as “real” problems.
According to Edens and Potter, “Visual-spatial representations may function as mental imagery, or in the “mind’s eye””(Edens & Potter, 2008, p. 184). Being able to visualize something really is being able to see it with the mind’s eye. I always find myself looking in the space, staring at nothing when trying to visualize something, as I am trying to see it with my mind’s eye. As it is widely seen that students are mostly interested in just finding the right answer and moving on to the next question. As Edens and Potter call these students the ‘number grabbers’ as they like to ‘compute first and think later’. I think in a situation as such, it is even more important for students to be able to visualize the problem before solving it.
I have chosen to apply T-GEM instruction framework and combine it with NetLOGO digital simulation introduced in this lesson. I think in my grade 8 honors class while teaching the graphing units where I introduce rate-of-change, I could use NetLOGO as the online simulator to help students visualize how a graph might get affected if the speed of one car changes compared to the other car at the constant speed. I will be using the “Traffic Basic” simulation on NetLOGO for this lesson activity starting with one red and one blue car.
Generate:
Step 1: Students are asked to identify the variables that affect the speed of the red car.
Step 2: Students are asked to get familiarized with the simulation and generate relationships between the speed of the red car and acceleration and deceleration
Evaluation:
Step 3: Students are asked to evaluate why are there two controls given to control the speed of the red car- acceleration and deceleration.
Step 4: Students are asked to evaluate the relationship between acceleration and deceleration and how they affect the speed in different ways
Modify:
Step 5: Students are asked to try using more than 5 cars at a time to experiment how the graph may get affected when the speed is played around with.
Step 6: Students use the new knowledge gained through the second step of T-GEM to modify the knowledge and find a relationship between acceleration and deceleration with more than 5 cars at play.
References:
Edens, K., & Potter, E. (2008). How students “unpack” the structure of a word problem: Graphic representations and problem-solving. School Science and Mathematics, 108(5), 184-196
Srinivasan, S., Perez, L. C., Palmer,R., Brooks,D., Wilson,K., & Fowler. D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15 (2), 137-141
https://www.netlogoweb.org/launch#https://www.netlogoweb.org/assets/modelslib/Sample%20Models/Social%20Science/Traffic%20Basic.nlogo
Anchored instruction is a technology-centered learning approach where students are given math and science problems to solve in realistic contexts. The first example of an anchored instruction that I came across was the Jasper problems. Looking at Globe, a few weeks later, it only fills me with joy knowing that we started at Jasper and have landed at Globe in a couple of decades. The first article that I read on “Mathematics in the streets and in schools” by Carraher and Schliemann, is about children selling food on the street and being super-efficient at doing mental math while when those children are asked to perform mathematical calculations on a piece of paper, they were not as efficient. These authors raise an important question at the end of the paper, “(are) schools out to allow children simply to develop their own computational routines without trying to impose the conventional systems developed in the culture?” (Carraher and Schliemann, 1985, p. 28). I think the answer to this question will be ‘yes’ for the majority of the schools, while there are few schools that use TPCKs such as Globe can be excluded from the list.
Therefore, I think the answer to the posed question is obvious that, yes, Globe is not only an example of anchored instruction but the definition of what anchored instruction should look like. Globe offers collaboration and learning for K-12 grade students across the world in 110 countries that not only benefit students but also the teachers and the admin. The website is designed to be very welcoming where “anyone” can join and be a part of something bigger than we can imagine. There are mobile apps that can record videos and take pictures that can be uploaded in the form of data collection to the website. In result to all of this, Herron and Robertson explain in their paper how “Using the Globe program to educate students on the interdependence of Our planet and people” is possible and happening. “Students recognized how people in the city and surrounding areas might be impacted by research on biomass. Many students focused on the benefits that could be experienced by the immediate community, while other focused on the impact of local industry” (Herron and Robertson, 2013, p.30). Students from all around the world are not only helping third world countries make a difference in their lifestyles or help scientists make new inventions, but they are making difference in their own communities as stated by Herron and Robertson.
Although, as I familiarized myself with the program- Globe, I was a bit skeptical about the data that is collected from a variety of sources, whether the data can be trusted or not. Penuel and Means’ article on “Implementation Variations and Fidelity in an inquiry science program: analysis of Globe data reporting patterns” addressed my point. After they analyzed data and surveyed teachers and students, they there may be some lack of confidence in the data reported. I think there must be some sort of filter that is applied once the data is received by the staff working at Globe to verify whether the data is acceptable or not.
However, other than the above, I cannot think of anything else that I could pinpoint to make this program any better than it already is. In the end, I think there is no option left for all of us but to go global with Globe and make a real difference in the world.
References
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British journal of developmental psychology, 3(1), 21-29
Herron, S. S., & Robertson, J. L. (2013). Using the GLOBE Program to Educate Students on the Interdependence of Our Planet and People. Creative Education. 4(A). pg. 29-3
Peneul, W.R., & Means, B. (2004). Implementation variation and fidelity in an inquiry science program: Analysis of GLOBE data reporting patterns. Journal of Research in Science Teaching, 41(3), 294-315
I am a person who speaks with her hands, so picking an article from the list given in the module was not so difficult for me. I chose to read Alibali and Nathan’s article on embodiment in mathematics and how teachers’ and learners’ gestures are the proof of it. It was very interesting to see that the authors described gestures as being the evidence for the body to be involved in thinking and speaking about the ideas expressed through those gestures. They even stated, “gestures are taken as evidence that the knowledge itself is embodied” (Alibali and Nathan, 2012, p. 248). I have always felt more comfortable expressing myself when I am able to use my hands and gestures while talking, it does not only help me express myself better but also helps me ‘make knowledge personal’. What I mean by making knowledge personal is that I feel that the main source of knowledge is that it comes from the inside of a person with probing from the outside, but by being able to use gestures and hands while expressing that knowledge, one can take that knowledge back inside. This is my definition of ‘making knowledge personal’ or one may call it embodiment.
Furthermore, it is sad to see that the prominent way of teaching in today’s world does not involve embodiment of knowledge at all. It is one person standing in front of the class, standing at the desk by the board, pouring knowledge out to the students sitting stationary in their seats. Winn puts it beautifully by saying, “The idea that cognitive activity depends on the context in which it takes place has been used as an argument for the ineffectiveness of instructional strategies that are employed uniformly with different kinds of students and in different contexts” (Winn, 2002, p. 5). I found this quote to be really powerful as it shows us the reality of today’s prominent teaching styles. The majority of the PCK in a typical classroom involves instructional strategies that do make learning to be a cognitive thing with no connection with the body.
As I was still thinking about the quote above and what Winn meant by the idea that cognitive activity depends on the context or how could one apply this in a math classroom, I came across an article that made me realize that it can be done. This article by Schaen, Hayden, & Zydney on “Now we have an app for that” talks about a project that involved elementary students to create their own apps to teach a math concept/ practice a math concept. I think this is a great idea to help students use their imagination and create something concrete that they can test their knowledge at. The TPCK taking place in this class is exceptional while the students are able to express their knowledge through creating an app that will reflect their knowledge on a certain subject.
I think I could use this website (www.tinytap.it) in my high school classroom where students create an app as a group where they can test themselves and others on certain topics learned in the unit. I think this is a great way to engage students in ‘hands-on learning’ while providing a TELE where students feel comfortable using technology to express themselves. This way students will be able to take ownership of their learning and at the same time ‘make learning personal’.
A few questions that I want to pose to my fellow learners:
References:
Martha W. Alibali & Mitchell J. Nathan (2012) Embodiment in Mathematics Teaching and Learning: Evidence From Learners’ and Teachers’ Gestures, Journal of the Learning Sciences, 21:2, 247-286
Schaen, R. J., Hayden, G., & Zydney, J. M. (2016). “Now” We Have an App for That. Teaching Children Mathematics, 22(8), 506-509.
Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114. Full-text document retrieved on January 17, 2013
There are multiple ways of using a TELE in our classrooms, although each TELE comes with unique features and qualities to it. The following table describes some of the features each TELE has and compares/contrasts them in the end:
| Anchored Instructions & Jasper | SKI & WISE | LfU and MyWorld | T-GEM and Chemland | |
| Main Features | Uses videos as the main tool to create problems that have real-life relevance | A teacher can use these online tools to create a whole lesson that fulfils multiple learning outcomes. | Problems are posed that have real-life relevance but very little information given to start with | Uses the online simulations to engage students in an inquiry based learning techniques |
| Learning Goals | Students feel more engaged with problems that are posed via videos and real-life relevance instead of using problems from a textbook | Uses scaffolding as one of the main tools to help learners who want to learn at their own pace. Students can go through these lessons multiple times for revision purposes | These tools engage students in problems that motivate students to inquire and access prior knowledge required for problem solving. | Students generate problems themselves by observing the given simulation and evaluate the results they arrive at. They get to modify the given simulation to learn further concepts. |
| Comparison/ Contrast | Jasper videos are videos that use real-life problems and turn them into interesting problems that high school students can solve. Similarly, LfU provides students with problems that can be seen in real life and be turned into problems that students can solve | SKI & WISE are not just tools that provide problems that students can solve but also help students learn a concept starting from scratch. | LfU and T-GEM require students to put their inquiry hats on before tackling the problem which makes these two TELES unique in their own ways | T-GEM is the only TELE that has a step-by step guide for teachers to follow in order to use this TELE in their classrooms. It makes me much more likely for a teacher to use a TELE in their classroom if there is a clear step by step guideline to apply them in their classroom. |
Synthesis: It is interesting to see how much all these TELEs have to offer to us in today’s world. All these TELEs give us a new hope for every child in our classrooms to be successful. These TELEs make sure that no child is left behind while they help students develop skills that will guide them through the rest of their life’s learning. These TELEs probe our students to be curious, motivated, collaborate, analyze data, and be independent. Jasper videos have given problem solving a new face as I, myself, was a student who hated textbook word problems because they were not relevant to real life at all. These TELEs give our students an opportunity to make their thinking visible and feel heard as they are able to express themselves in multiple ways. There is no bigger blessing to a child who feels they don’t understand everything in a classroom to be able to access a WISE lesson online and review material at their own pace.
With all these qualities that these TELEs have, one must think why are these TELEs not widely used in our classrooms. This module has been an eye opener for me given that I consider myself a teacher who uses technology in her classroom on a regular basis. Yet, I had never heard of any of these TELEs ever before. It is unfortunate that we have such great resources available online, some free of cost, and we don’t even know about them. Whether it is the lack of advertisement of the tools available online or the resistance to use on teachers’ part; our students are the ones that are suffering. No teacher goes to school thinking they are not going to do the best for the students today. All teachers do do their best but what is lacking or stopping these wonderful teachers from using these amazing TELE designs available online. It is interesting that TELEs such as T-GEM and LfU are pedagogical techniques that teachers can simply apply in their classrooms without having to deal with heavy duty technology in their classrooms. I just wish more teachers knew about these TELEs and we were able to help each child achieve their maximum potential possible in our classrooms.
I have had the opportunity to teach an enriched class of grade 8 students who are expected to learn a little more than what cover the curriculum. Thinking back to the time when I was teaching the surface area and volume unit, I wanted to do something more than just a few difficult problems at the end of the unit for these students. I decided to get my students to inquire about the relationship between a prism’s surface area and volume. After looking at the results of this activity, I think I had overestimated these students’ abilities as this lesson did not go so well. I ended up using some difficult problems at the end of the lesson to make sure the students got something out of this lesson.
Anyhow, looking back at this experience now, I think T-GEM would have been a great TELE for me to use for this lesson. Instead of asking students to inquire using paper and pen, including technology would have been extremely helpful. After doing the readings for this lesson, I realized that T-GEM would work great for this activity as it will require an online simulation and some probing on the teacher’s part during the activity and students will be putting on their inquiry hats while comparing numbers and getting deeper understanding of the concept.
The main outcome of this lesson is expected to be that students are able to get a visual understanding of how 3D shapes change when the dimensions are changed and how to use minimum surface while getting maximum volume of a 3D shape. My students were not able to do the latter part using paper and pen as it required an overwhelming number of calculations that ended up getting the students frustrated.
My 3-step T-GEM cycle plan includes an online simulator- http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/
This online simulator allows you to change dimensions of a 3D shape and instantly gives you the surface area and volume of the shape. I will use this online simulator to help my students understand the relationship between the dimension change and SA and volume. Their task will be to minimize SA while maximizing volume of rectangular or a triangular prism using this online tool.
I think T-GEM is a great resource for activities as such and I am excited to try this out with my grade 8 honors class next year. Best thing that I like about T-GEM is that it is a full package. It starts with inquiry based learning and probing students to inquire about new things on their own to get their feet wet, then it gets students to make relationships using their inquiry knowledge and leading them to be able to modify the knowledge that they have gained in this process to be able to apply to a new scenario. And all of this is done in a TELE setting which really makes this whole process much more efficient and engaging for the students. T-GEM really is a gem!!
One of the resources that I had recently come across, with the help of a classmate in this class, was also mentioned in lesson 3 on canvas, realworldmath.org. It is a great resource to take learning outside of the classroom and falls right in line with Lfu principles. This website provides certain lessons and activities to help with the delivery of content and is embedded with inquiry in it. I would use the lesson on Measurements for grade 8 students to understand Surface area unit of their curriculum.
This lesson on Measurements on realworldmath.org fulfils the three steps of Lfu model listed by Edelson in her article. “The goal of the Lfu model is to overcome the inert knowledge problem by describing how learning activities can foster useful conceptual understanding that will be available to the learner when it is relevant” (Edelson, 2001, pg. 356). This lesson on Measurements, along with the other lessons on realworldmath.org, help students overcome the inert knowledge problem by creating an atmosphere for students to see how useful this learning can be. First step that is described in Edelson’s article is to motivate. Using the lesson on Measurements- first example of complex area will motivate my students to ask themselves, what would the surface area of a complex area like this would look like. My students will be curious about finding area of surfaces that are not just one shape (a square, rectangle, triangle) but a combination of shapes. My students will only have knowledge of how to find surface area of basic shapes before looking at this problem. At this point, students will be asked to observe and try to see if it is possible to find area of a surface that is not explicit ally a shape that they can name. This will fall under the second step of Lfu of constructing knowledge. After this inquiry-based task, students will receive direct communication to help them reach the solution; where the students who did not figure out on their will be assisted with realizing that it is a combination of squares and rectangles. The third step of Lfu says that students should be able to apply their knowledge, which students will do at this point and divide this shape into squares and rectangles and find the surface area for themselves. Students will be asked to reflect on this problem in the end where students will be expected to have understood that the area of a surface can be determined if the surface can be divided into shapes that we know of.
“If we conceive of both science and learning as social endeavors with shared intellectual ownership, how should we assess students’ progress toward “thinking like scientists”, or “doing science”? (Radinsky, Oliva, & Alamar, 2010, pg. 620). This quote triggered a memory in my memory-lane where I was observing an elementary school teacher before doing my teaching degree to get some volunteer hours in a classroom. She was a great teacher with great teaching techniques but I still remember her using the words, “put your math away now, we are going to ‘do science’ now”. I remember these words did not settle well with me back then but I did not know what was so wrong with saying “do science now”. “In traditional science classrooms, content and inquiry skills are taught separately through separate learning activities” (Edelson, 2001, pg. 356).
Edelson did an amazing job at defending today’s science teachers feeling torn apart with the amount of pressure put on them from the administration to incorporate technology and inquiry while delivering a high density of content in a classroom; and all of that without any real support to help teachers achieve all of this. Edelson makes a great point by noting that traditional science teachers think that content and inquiry skills must be taught separately, which is why they would refer to “thinking like scientists” as “doing science”, in my opinion. ‘Doing science’ indicates that a student must ‘do science’ for the given period of time and then forget about it once they leave the classroom, leave the learning behind because that is where they ‘do science’. On the contrary, when the students are motivated to “think like scientists”, they are forced to take that with them outside of classroom because it becomes a part of their thinking process. We need our students to take learning outside of the classroom, virtually and physically. Lfu is a great teaching framework that provides us with tools that can help teachers encourage students to take their learning outside of the classroom.
Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385
Radinsky, J., Oliva, S., & Alamar, K. (2009). Camila, the earth, and the sun: Constructing an idea as shared intellectual property. Journal of Research in Science Teaching, 47(6), 619-642.
I have had the opportunity to work with students who have designations in terms of learning disabilities; therefore, they come to the learning center during their study block or after school to get extra help. I feel that using WISE with my learning center students would be a ‘wise’ idea to help them understand some of the concepts they did not understand fully in class. I would be using WISE as a supplement tool for students to re-learn or perhaps review what they learned in their class. Based on my experience, most of the times these students think that either the teacher went over the material in class way too fast or they were just not paying attention when the lesson was taught. Either way, it shows that they are fully capable of understanding the concept that they missed if taught in a different setting at a different pace using a different PCK.
Using WISE would help these students have a better chance/ another chance at learning the missed material or perhaps the misconceptions that may have taken place the first time they learned about it. WISE would also be a great tool for these individuals as most of the WISE lessons are interactive and one can learn at their own pace in their own time. One of the best thing about WISE lessons is the scaffolding happening starting from the beginning and question prompts as the students go through the lesson to support the learning. My students would benefit a great deal with SKI taking place in WISE lessons as they can go back to the content to re-learn the material if they get the answer wrong for one for one of the questions as they go through the lesson.
I would ask my student to start by going over the table of contents for the lesson, so they see some of the familiar terminologies that they have seen earlier in their class. I chose to edit the “Plate Tectonic” lesson as I have taught this lesson to an Earth science class before and am familiar with the content knowledge in this lesson. This lesson starts with a slide on “Did you feel it?” asking if you felt small-scale earthquakes during the day. One change I would make is to ask my student to google “earthquakes in Vancouver” and see for themselves that how many small-scale earthquakes actually take place every day that are rarely felt by us. The reason why I would make this change is to make this lesson’s beginning a little inquiry-based. Instead of telling them, students learn better if they see it for themselves.
Another change I made in the lesson was to add a “modeling” question at the end of the second lesson’s slides. The question is to ask students to draw “continental-oceanic” vs. “continental-continental” plates on a piece of paper and write about the difference between these two plates on WISE. The reason why I added this is because first, students use “model as a communication tool” (Gobert, Snyder, & Houghton, 2002, p. 5) and second, it helps students test themselves and be confident about certain knowledge. In my setting, where I will only be working with one student at a time, comparing the model with other models would not work. Although, I think students learn a great deal from their peers by evaluating their work. To conclude my lesson with this student, I will ask the student to compare their drawing with the one on the previous slide and point out the differences and make corrections.
Gobert, J., Snyder, J., & Houghton, C. (2002, April). The influence of students’ understanding of models on model-based reasoning. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New Orleans, Louisiana.
Being a young teacher also means that I was in a high school myself not too long ago as a student. As I was reading articles and watching Jasper videos for this lesson, I could imagine myself being in a classroom where these videos were shown to “anchor instruction in the context of meaningful problem-solving environments that allow teachers to simulate in the classroom” (Cognition and Technology Group at Vanderbilt (1992b), pg. 294). As I can relate to the students who were shown these videos in their math classes, I can also understand what problem did the Jasper material was trying to respond to. One reason I can pinpoint is to give an answer to those students who are often seen saying, “When am I ever going to use this in my entire life?” to a teacher in their math class. These videos are great “answers” to the question posed by many teenagers in our high school system these days. This question has made me re-design some of my lessons as a teacher since I wanted to be prepared if this question was ever asked in my classroom.
The first article I read in this lesson was on helping students with disabilities learn mathematics using technology and I don’t think the issue that I have mentioned above was discussed at all in this paper. The main focus of this paper was to understand why do we use technology to support student mathematical learning. Most of the reasons went along the lines of building computational fluency and conceptual understanding as well as creating mathematical representations. I agree that technology can play a big role when trying to represent mathematics which can, in return, help solve the issue that I have brought up in this discussion. Mathematical representation using technology can bring ‘boring textbook problems’ to life and help students understand why they might use this again in their life. My second reading was also related to helping students with disabilities learn mathematics using technology by Russell Gersten, this is an elaborative case study that includes researching multiple cases in order understand best mathematics instruction for students with learning disabilities. Again, this article focuses on how technology can help students with gaining a better understanding of mathematics but fails to focus on the visual impact of technology on students in a math class.
In today’s world, we have multiple online sources available that can help us turn our classrooms from “boring textbook question” oriented classrooms to classrooms that portray the real world through real math problems. We, as educators, are responsible for making our students ready for the world where they can tackle real-world problems with the “real-world” math problem-solving experience they have gained in their high school.
Cognition and Technology Group at Vanderbilt (1992b). The Jasper series as an example of anchored instruction: Theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.
Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development. Retrieved December, 12, 2013 from Google Scholar as a pdf.