Category Archives: A. Video cases

In my previous post on assumptions I presented 5 ideas that I thought lead to quality use of technology in the math and science classroom. This week, I viewed video 1 and video 6.

Video 1 takes place in an advanced STEM class where technology is paired with various concepts from physics and chemistry to find creative ways to solve existing problems. Video 6 takes place in a middle school setting in which students’ pair technology with their existing work. They use the technology to provide alternative assignments and deeper learning activities.

In watching video 1 specifically, the once idea that really jumped out was concerning the foundation of student understanding. Repeatedly in the videos, students comment on how they only understand what is happening because of a previous course. Teacher M even comments that some foundational knowledge is missing, which is ridiculous. As a result, he supplements the curriculum with other knowledge he thinks the students should know.

It is interesting seeing how video 1 features students that have benefitted from rich technology programming and video 6 presents a school that is newer in their tech-teaching journey. In my analysis I will try not to compare the two in a harsh manner as both are doing their best with available tools and training.

I will evaluate both of these videos within the 5 categories I presented previously.

Technology use in the classroom todays needs to flow seamlessly with other work. 

Video 1: Technology in the classroom flows seamlessly because the class has a focus on technology. Teacher M is also of ‘super teacher’ caliber and has a deep understanding of all learning areas, so he is able to direct students towards technology that is best suited for their application.

Video 6: This case sees technology essentially acting as an add-on to the existing teaching practice. While this might not be considered seamless, it appears well received by students and they enjoy the opportunity to learn (and present learning) in various ways.

 Good technology use should take risks.

Video 1: Here we see technology taking all sorts of risks. Students are designing Arduino based temperature control devices. They have a high likelihood of failing, and are fairly advanced…but students are trying it! Teacher M also provides realistic and challenging assignments for students that require them to take risks.

Video 6: The risks taken by this teacher are quite different. He comments on how the funding for technology was not easy to acquire. If his students don’t produce any sort of successful or attractive content, the well will dry up quite quickly. His risk is more school-organizational than video 1 but still very much a daunting reality. In trying to help his students thrive, he runs the risk of himself failing in this endeavor.

Technology must provide opportunity for differentiation.

Video 1: There are a variety of different projects and challenges for students. There are also different roles for group members within these projects. This provides students the opportunity to do ‘different things’ with technology, but doesn’t necessarily see it used as a differentiation tool.

Video 6: One of the students interviewed in this video directly highlights the fact that different students learn in different ways. Through technology, students have a change to learn in an increasing number of ways. It is very clear that in this case technology is most definitely a differentiation tool.

Technology should be taught.

Video 1: In this video students comment on learning concepts in past years. The teacher then builds on this knowledge and provides a connection to technology. It is expressly clear that the learning students are doing in this class could not be accomplished if not for the chemistry/physics/STEM concepts that were taught in previous years.

Video 6: The different interviewees in this case communicate that technology is being taught directly to students. This is in large part due to the fact that the technology is fairly new to the school and students do not have experience with it specifically. That said, it is also mentioned that students do have existing knowledge with technology in general, as many are often listening to their iPods in class.

Technology shouldn’t merely be a replacement for the current status quo.

Video 1: Technology is used to enhance, deepen and grow student understanding of previous concepts.

Video 6: The technology is used in-addition-to previous teaching, and not as a simple straight across replacement.

Conclusion:

While I feel both schools are doing a solid job with the available technology, it is hard not to be impressed by what is happening in video 1. Teacher M is a rock star, and is able to clearly communicate problems and solutions to students in a way that leads to truly impressive results. Video 6 has a school newer on the journey, but trying hard and accomplishing what they can.

As a final closing note, access to technology is one major question that came to mind when comparing these two videos. The school in video 1has programming classes, STEM classes and intro computing. It seems that there is an abundance of technology within the building, and teachers are doing a great job of managing it. Video 6 sees the teacher having to raise much of the funds himself for technology. From the outcomes occurring in each classroom, there does seem to be something to ease of access and student accomplishments.

When watching these video cases, I was struck by how many of the arguments and concerns raised then are the same today.  On the FOR side, tech is seen to give consistent, dependable results, and instant feedback, allowing opportunity for corrections (Teacher B); tech saves time from tedious data analysis and plotting to increase deeper learning (Teacher A) and gives the opportunity to engage students while developing motivation and transferable skills (Teacher F).  Teacher E talked about the opportunity for collaboration and the feeling of ownership.  On the AGAINST, issues that were raised were a loss or reduction of hands-on lab skills (Teacher B), tech as a barrier: needing to learn tech as opposed to learning the content (Teacher B, students 9, 11, 15), financial costs and support (Teachers F, D & A), and the greater time demands (cases 5&8).

For the most part, it seemed that the barriers were on the side of the teachers (uncomfortable with tech, no support, finances, limited time) while the benefits are mainly student oriented (engagement, higher order problems, deeper learning, collaboration, transferable skills), which leads me to wonder how could we not use at least some tech?  If we don’t, are we becoming barriers to the students education and engagement?

On the other hand, I see some practical questions that should be addressed:

1. Using extensive tech requires students to learn many tech skills and programs. How do we maintain a balance between learning the tech without limiting the content?
2. How can we engage all students with effectively with limited resources? Is there an ideal ratio between # of students and # of devices/tech?
3. For level 3 classrooms, where students are self-directed, the common understanding is that students are suddenly motivated and engaged, because those are the ones who are interviewed. In my experience, there are always some students (usually teenage boys) who are not engaged, interested, or motivated about ANYTHING in school, regardless of subject, content, or teaching method.  Are they at greater risk or falling through the cracks, creating distractions, or needing management in this type of setting?  Some students do better in a structured setting… and for some the teachers want it!  Thoughts?

This year I have 8 laptops in my class, which I use a lot for collaborative work and digital reflections/discussions, etc.  I have found that it takes a LOT more classroom management to control the off-task behaviour of a few of my students, to the point where it almost ruins it for the rest.  Having teacher-centered gives that element of control needed for those individuals.  Halfway through the semester I gave a survey to my grade 12’s and they indicated that the best ratio is 2:1.  This allows for some collaboration, while not having any “fringe” people feeling left out or uninvolved.  As for motivation and engagement, I have found that the greater diversity of learning strategies, the better, but the amount of new tech/software should be limited, rather for the most part, existing tech skills should be built on and used in new and creative ways.

In my previous post I mentioned that effective use of technology in math and science should be used to enhance student learning and not be used to keep students “busy”. There should be specific objectives and a purpose for why technology is being used within the classroom.

Watching Teacher S in Learning Environment 5, she demonstrated an effective use of technology. She was very comfortable using it and mentioned that her class is “part of a team”. They are able to work together effectively and obtain good results and demonstrate their understanding. The students work together as part of project based learning which creates opportunities for collaboration and creativity. Teacher S also mentioned that her students are “tech savy” and typically troubleshoot and figure things out. She mentioned that a challenge is the language barrier with ELL students, but with using technology this helps to break this barrier. The students were excited and showed great interest and pride in their learning.

The retiring teacher discussed how she gets “extremely frustrated”, “doesn’t have knowledge” and “doesn’t have time to use the computer”. She mentions that her students know what they are doing and she often relies on them to teach and help each other. She mentions that she isn’t comfortable and requires time to practice. In my previous post, I discussed how professional development is great for educators to attend, but most require time to practice and explore. Thinking about myself, I find that I attend amazing professional development opportunities but don’t have time to practice/explore and I am very comfortable using technology, so I can completely understand how this teacher felt. An example from my work is one of my colleagues was close to retiring when our team was involved in an iPad inquiry project. She shared the same views as the retiring teacher. What really helped was our team would plan weekly lunch collaborative meetings to teach her and let her explore so she could learn and ask questions. The new teacher in the video also discusses how she collaborates with her classroom neighbour when she chooses to integrate technology. She also finds there isn’t enough time to practice and believes the teachers should receive training in pre-service courses. At our school we have had weekly “tech” lunches where teachers can drop by and share how they are using and integrating technology within their class and it’s an opportunity for educators to collaborate and practice.

In Case 8 (Learning Environment with Teacher E) it was great to see how the pre-service teachers were practicing with Slowmation and learning the value of it for students when comparing it to a textbook. They mentioned that it’s engaging for learners, visually appealing and works well for including ELL students.

I believe schools should collectively work together so everyone is comfortable using and integrating technology within their practice as we know it has value-added. I believe it can be a simple as a weekly drop-in lunch sessions where educators practice, share and collaborate. It worked well at my school and was supported by admin.

I  really enjoyed watching Case #1 and #2 as they both pertain to my role as a senior math, calculus and physics teacher.  I found Case #1 particularly interesting as I had collaborated with this teacher on two different ETEC projects in the past year.  I had always found this STEM program quite interesting and inspiring and enjoyed gaining an appreciation for his workspace and watching how his students engage with the program.  Below are some themes that stuck out with me:

Relevance:

My years of experience teaching math and physics onboard a sailing high school have reinforced my belief that students learn best when they recognize the relevance and applications of what they are learning.  In this case, students are working through problems and then testing their conclusions in real life.  Awesome!

Guide on the Side:

Furthermore, much of the knowledge the students were acquiring did not come from the teacher; it was the product of self-directed inquiry and discussing with more-knowledgeable peers.  The role of the teacher here is to provide enough information for the teams to get started and then offer direction and support while holding each group accountable to their learning when necessary.  

Quality vs Quantity

As opposed to my rather traditional classroom where we might solve a dozen or so questions in a class, these students were solving one big question over the course of a long period of time.  

Resources

Students had access to superb materials, resources, and tools.  In one video, we see the teacher showcase the material testing equipment suitable for testing the limits of various materials.  We also notice students are using computers and other electronics to develop code.  I appreciated how digital technology was connected with hands-on materials.

This case definitely left me with a few questions concerning management and accountability of learning.

1. How does the teacher manage, support and direct so many teams while holding each student accountable to the course objectives (particularly with less motivated students)?
2. How are the mechanics of physics/math assessed?  Or are mechanics less important?

I recall the teacher once saying during one of our conversations that he does struggle with class control at times.  Not that students are often misbehaving, but more struggling to know where each team is at.  In a traditional classroom, the teacher is able to manage learning expectations and the pacing of course content fairly easily.  Here, the teacher really needs to trust that the students are intrinsically motivated to solve problems using the tools available to them.  For this program to be successful, the teacher needs to understand what the students are able to accomplish, understand the tools and resources available and build a class culture that supports inquiry and curiosity.  

The use of digital technologies and hands-on material definitely ameliorate conceptual challenges in understanding physics and material design.   Students can feel what happens to the strength of the materials when they modified or rearranged.  Learning needs to grow from prior knowledge and experience and what better way than have students constantly test their most intimate form of knowledge, their intuition.

“Where is there room in the curriculum?” – Teacher D

In the case videos, it is apparent that technology integration required more learning time and commitment. Students are spending time to explore technology and develop their competencies as they deepen their understanding of learning concepts. In preparations for standardized testing, educators have to be extra mindful to ensure that the projects cover expected curriculum objectives. Thus, allowing their students to be prepared for standardized testing.

Limited time to cover content area is also a consistent theme in the primary classrooms. Similar to the need of preparing students for standardized assessment, practicing basic literacy also competes for students’ time. As a grade 2 teacher, the students are just beginning to read and write. They are still in the early stages of developing and polishing their basic literacy skills. Should typing be practiced like printing? Given that it is more difficult to navigate a new communicative space students should be explicitly taught how to decode and navigate through digital information (Bolter, 2001). The important question is how can teachers balance these curriculum demands? It is likely that flipped learning is favorable in these situations in order to meet additional curriculum expectations. Teacher C in middle school life sciences remediates limited lab time by asking students to complete tasks as homework. Project-based learning requires time and commitment from educators to mentor and watch the students learn digital literacy competencies and to practice content knowledge.

Additionally, the lack of basic literacy skills makes it harder for them to solve problems when using technological tool. A pre-service teacher in learning environment 3 suggests that young learners may only be practicing ‘recognition based skills’. Some technological tools are substitution in disguise. Nonetheless, with a firm grasp of literacy, students are better at regulating their learning with technological tools. Students are also more able to independently troubleshoot and problem solve.

What other plausible solutions are available to assuage literacy gaps and limited time?  

Strategy 1: Collaborating with Others

Interactive learning in a small group is ideal when students are exposed with unfamiliar technology. With technology, students can engage in “spontaneous helping and teaching”, turn taking and competition (Clements & Sarama, 2002). Together, students can also discuss and reflect about learning concepts.

Strategy 2: Utilising Personal Learning Plans

A rather radical plan, one plausible solution is the abolishment of grades levels and modifications of ‘standardize’ testing. Skill based and mastery based learning should be key pedagogical philosophy of current education system. Students should progress in various skill-based groups depending on their level of mastery. Consider Altschool: https://www.youtube.com/watch?v=N8ZrUuZjsow

Strategy 3: Enhancing Digital Competencies

Literacy learning is as important as digital literacy. Therefore it should be taught at the same time as other basic skills. Some regional or national polices recognize this, thus making changes to the curriculum to assuage the need. Recent changes in the BC curriculum recognizes of the value of explicitly teaching multi-literacies. For example, the curriculum moved away from content-based learning to an inquiry approach that prioritizes viewing and demonstrating proficient use of multi-literacies. This may also explain why families feel that Altschool’s personalize learning is insufficient. Robinson (2017, November 21) writes that families are leaving Altschool due to the fact that their children are behind grade level expectations. Perhaps Altschool’s personalized learning should be coupled with STEM learning. This may also allude to the differences in the social understanding of student achievement.

Strategy 4: Developing Educational Reforms

Curriculum expectations may ease some expectation concerns. Since this changes how students are assessed, it should be reflected in national assessments. This refashions the fundamental understanding of learning, schooling and knowledge. Internationally, students are evaluated with standardized exams. This then is inconsistent with the notions that STEM projects promote. Students are developing a battery of skills to solve challenges. Instead of provincial exams, students should have the option to be evaluated through STEM projects.

Moreover, Knapp (1997) suggests that education alignment is key to successful reforms. More specifically, district level support and more targeted outcomes directly influences. Consider nation-wide e-learning reforms like ICT strategic plans in Bhutan and Nepal. Local and national support is also a key factor in ensuring a higher success rate of the strategies. Bhutan and Nepal budgeted over 16.5 million to support their strategies. Infrastructural upgrades and professional development opportunities for educators are key strategies that Bhutanese and Nepalese government uses in order to support their vision.

Conclusively, personalized learning coupled with educational reforms and a strong need for social learning is key for 21^st STEM learning. While this may be a romantic notion of what education should be, it provides clear directions as to where education should be heading. It is evident that current education landscape has the potential to continue due course, however, without appropriate changes in the local and national level, current challenges remains unchanged.

Reference

Bolter, J.D. (2001). Writing Space: Computers, hypertext, and the remediation of print. Mahway, NJ: Lawrence Erlbaum Associates, pp. 3246, 7798.

Clements, D. H. & Sarama, J. (2002). The Role of Technology in Early Childhood Learning. Teaching Children Mathematics, Vol. 8, No. 6, Focus Issue: Learning and TeachingMathematics with Technology (FEBRUARY 2002), pp. 340-343

National Council of Teachers of Mathematics Retrieved from: http://www.jstor.org/stable/41197828

Knapp, M. S. (1997). Between systemic reforms and the mathematics and science classroom: The dynamics of innovation, implementation, and professional learning. Review of educational research, 67(2), 227-266.

Government of Nepal. (2013). Information & Communication Technology(ICT) in Education Master Plan 2013-2017. Retrieved from http://www.moe.gov.np/assets/uploads/files/ICT_MP_2013_(Final)_.pdf

Robinson, M. (2017, November 21). Tech billionaires spent $170 million on a new kind of school — now classrooms are shrinking and some parents say their kids are ‘guinea pigs’. Business Insiders. Retrieved from http://www.businessinsider.com/altschool-why-parents-leaving-2017-11

Royal Government of Bhutan.(2014). iSherig Education ICT Master Plan 2014 – 2018. Retrieved from http://www.education.gov.bt/documents/10180/10994/Education+ICT+Master+Plan+2014-18.pdf/00392bc0-0ed2-47c9-9e2e-ed30e23ccf8f?version=1.0

Case 5: The clip is of a lesson on space exploration with a grade 6/7 split class. Includes Teacher A, B, C, and students reflections

Case 8: This video is of elementary teacher candidates learning how to use “slowmation” to model processes in science.

I chose to discuss the content in video 5 and 8, as they were the closests to a lower elementary classroom. Most of the these applications used these (Kid Pix, Stop Motion, garageband, Apple photo books) I have used with 7-9 year olds.

I thoroughly enjoyed watching Teacher “A’s” interpretation of her experience with technology in the classroom, for instance,  she was “surprised to see the results but more surprised how good the results [were]”. This constructivism approach and technology can work together to aid this learning process. As Teacher “A” stated, learning with technology “promotes understanding “ and the enjoyment of learning transcends into other subjects. Furthermore, she found ELL students had difficulties with the language component of the assignments, but with the assistance of technology these students are “able to express their understanding other than written language.” I appreciated Teacher A’s ability to release the responsibility and to be able to coach and scaffold her lessons. She is very passionate about educational technology, and the many things it can do for education is apparent.

On the other hand, Teachers “C” and “B” were both reluctant to embrace the influence of technology on students learning. They articulated the need for more time to learn the functionalities of the technology and their inability and inexperience to troubleshot to help their students. I understand that some teachers harness this powerful tool for our classrooms, just as there is technology is challenging to work with. But some are amazing! Teachers can knock down the walls of their class and ask for assistance from colleagues and other students to expand our knowledge. As teachers, we need to model how to seek help with technology and discuss ways to troubleshoot.

In case 8, the elementary teacher candidates are already learning that educational technology is the tools that we integrate into classrooms as part of empowering learning. You can see the excitement using slowmation and they realize how technology can enrich the students learning in any subject area. They are first hand experiencing how technology can get more students engaged, improve collaboration, and most importantly make learning fun!

The first video shows good use of technology, including personalized teaching, student activation, student self-regulation, and cooperative learning. This mirrors some aspects we had discussed in lesson 2.1. How is this realized in the first video case? Personalized teaching is supported as students are able to select the tasks they want to work on, and by choosing their own pathway toward a solution and by working at their own pace. Student activation is supported, as students get open-ended questions and have to explore different solutions on their own. One student confirms this by saying that they are able to make experiences on their own, which is much more effective in his opinion than regular classroom teaching. Self-regulation is supported as students are supported to define a research plan with aims and tasks, but also to be flexible to adopt this plan if necessary. One teacher confirms this by saying that they teach kids to help themselves. Finally, cooperative learning is supported by group work. As a teacher explained, students have to work together as a group, not individual, to be able to solve the problems. Only the technology itself is not always seen as user friendly and easy to use – a teacher explained that often, the machines and computers will not work properly, which demands a high level of flexibility from teachers and students. All teachers agreed that in this lab, important soft skills are taught.

Based on this video, I want to extend my list on aspects of good use of technology, and this is: flexibility. Teachers must be flexible to accommodate to the learning process of the students and to unexpected barriers such as failing computers. One teacher says that it is not any more about designing lessons, but about flexibly monitoring students what they need, and to support them.

Some of the other videos show low technology integration into classroom. Video 5 shows teachers who are reluctant to use technology because of “lack of time”, “lack of training” or “lack of support”. But here, for me, there is an open issue: Is this reluctance to embrace technology really only a problem of time and training and support? Thus, will it really be sufficient to give those teachers more training and more time? Or do some personal attitudes versus technology (such as technology anxiety) would still prevent them to adopt technology despite training and support? On teacher said she had attended several professional developments courses, but never tried to apply the new knowledge in her classroom ….

Do we have to accept that there we always “laggards” in any technology innovation …? Or does it mean we need a special professional development initiatives and support structures for these reluctant group of teachers?

Elske

This week I choose to explore case 5 and case 8, as they both focused on upper elementary grades and this is the grade level I have spent the most time in.

I found it very interesting, and relatable, that in case 5, many teachers from the same school could have such differing opinions and experiences with technology. In my post to Lesson 2 Activity 1: Unpacking Assumptions, I wrote that good use of technology enhances and doesn’t just replace something else. One teacher at the school in case 5 was using laptops to create podcasts and soundscapes – in doing so this enhanced the experience for the students. Further, I loved how this teacher didn’t think of herself as the leader but instead a “guide on the side.” One mistake I that often think teachers make is not introducing a new technology to their class unless they are completely confident with it. This does not demonstrate risk taking or promote the mentality that we are all make mistakes and we can all learn from each other. The teacher in this clip focused on all the benefits that she has witnessed technology fostering – language use, promoting engagement and increasing understanding.

At that very same school there were two clips of teachers who were overwhelmed when using technology and didn’t feel confident using it in their classrooms. Interestingly, these clips came from a retired teacher and the other from a newly qualified teacher. They both cited time and support as obstacles to technology use.

In case 8 the student teachers were making stop frame videos to explain a Science topic to elementary students. The professor of this class explained that he wanted his in service teachers to have technological tools that they could actually use on practicum. I believe this to be so important. This makes me think back to my Bachelor of Education degree, which was only 7 years ago. Although I found the program very useful, I can probably count on one hand how many practical, usable technological ideas I came away with. This was partly due to the content of the courses, coupled with the fact that my mentor teacher was very hesitant to use technology. The teaching practicum could be an incredibly valuable time to get student teachers excited about educational technology but what happens if they have obstacles like reluctant mentor teachers? A lot of responsibility then falls on a nervous, first time teacher, which seems not quite right. What can universities do to help student teachers overcome these challenges?

The last point I want to make is that in case 8, many of the student teachers claimed that they may not use stop frame animation in their classrooms because of the time it took – despite claiming the educational benefits for EAL learners, different ability levels and how this kind of project allows students to take ownership over their work. I think this issue of ‘we don’t have time’ comes up over and over again, and I sometimes find myself thinking this. What is important to remember is that a task of making a stop frame animation video about curriculum content is not an add on – it’s enhancing and enriching the curriculum and who doesn’t have time for that?! Technology has to be really fully seamless and integrated into everyday use to believe this view. But the question is, how do we get to this point?

I have to admit I was overwhelmed this week when I was faced with eight (8!) case studies to explore. Thankfully most were quite short, clocking in at less than 30 minutes, and they were actually interesting! I was a little judgemental when the videos seemed a tad dated, but what technology doesn’t seem dated almost immediately these days?

Example 1: I traded in my Pixel last month for a Pixel 2. The original Pixel was only released in October 2016 – barely a year ago.

Example 2: Last term I created tutorial/screencast videos for D2L to help my staff get better acquainted with its basic functionality. When we returned this term D2L Brightspace had upgraded to Daylight, making all my tutorials obsolete, or at least annoyingly dated – nothing looked quite the same.

My point is that I was once quick to judge a video by its video quality and perceived production decade – perhaps our generation’s higher-tech version of “judging a book by its cover” – but these days I’m much more interested to see if the content remains relevant. Often, much of it does, once you get past the initial reluctance.

Among the various cases offered I chose to focus most closely on Case 2, which deals primarily with introducing graphing calculators (namely the TI-83) into class back in 2004 or so. This case struck a nerve because I’ve had conversations and meetings with my department as recently as last Tuesday about the role of the calculator in classes. Opinions range from “they should do it all on paper then check their answers with the calculator!” to “let the calculator do the nitty gritty for them so they can tackle more complex problems!” to “why buy this $240 (in Doha) for a TI-84+ when all students have mobile devices and can get Desmos for free?!”… that last one was me…

Anywho, without further ado:

What are the underlying issues and why are they issues?

From my perspective, the first underlying issue for this case was the fact that it is significantly cheaper to buy a class sets of TI-83 graphing calculators (which the teacher referred to as computers, and he’s not wrong) than to buy a class set of desktop computers. This is a pertinent issue, one even more pertinent circa 2004, when smartphones were not as widely used. Not only do students and their parents rarely have “money to burn” per se, but neither do schools and school boards. If they can choose graphing calculators for mathematics classes for each student instead of expensive desktops, or even laptops, it may help ease the financial strain. One caveat here is that a graphing calculator, like any tech, is not a magic bullet. It must be thoughtfully chosen to meet a specific need of the students. For example, examining course requirements could reveal that a much cheaper calculator like the “Casio Scientific Calculator fx-82AU PLUS II” could do most of the same job at half the cost.

Another underlying issue in this case was that leveraging a tool like the TI-83 can help students from getting “lost in the math”. Instead of trying to “get a number” at the end of a series of steps, the teacher was able to ask deeper questions and the  “technology made [the students] comfortable to push this question to the limit”.

How would I explore a response?

Let’s not forget that ”better learning” using a tool like the TI-83 doesn’t happen automatically. Training is required for teachers to understand how to best leverage the tool for the benefit of their students and their unique learning contexts. As was said by Teacher F in the case study, “teachers do need to understand as much of technology as possible to make sure that you are able to ask questions of an appropriate level to get the mathematics out”.

I’d also like return to an earlier point on how TI-83 is a notably cheaper choice for classrooms than individual desktop computers. While this still mostly holds true, there exists stiff competition and excellent alternatives. Chromebooks are now becoming comparable in cost to calculator like the TI-84+, and there exist free mobile apps that can do almost everything that the best graphing calculator could do in 2004. Finally, why focus on a single expensive tool like a TI-83, or invest in static desktops for the classroom, when we could focus on leveraging students’ own existing mobile devices using a Bring Your Own Device model?

What further questions does the case raise?

Many of the questions that came to mind during this case were ones about students. Did the introduction of the graphing calculator increase student engagement? How did students that took math courses using the tool fare against past students who did not have it? Did the school start using the TI-83 for all their math classes? We heard from several students who were doing exceptional work with the calculator (Boba Fett represent!), but how did the weaker students feel about using a tool with so many buttons and functions? Where are all these students now, and what tools do they use for math problems? What would be the 2018 version of Teacher F’s mathematics technology?

How might the issue that is raised exacerbate or ameliorate a conceptual challenge held by students?

I think that, for most students, once they wrap their head around what a graphing calculator can do it opens the doors to a huge world of conceptual understanding. Ideas that could once only be explained in words, textbook diagrams, or time-consuming hand-drawn graphs could now be visualized with nothing more than a few button taps. For topics like curve sketching, graphing tech allows intimidating, abstract or, confusing equations like

x² + y² = 1

x² + y² = 2

x² + y² = 4

to be seen for what they really are: simple circles.

All in all I feel like using graphing calculators, especially recent free graphing software like Desmos, is nothing but a good thing. I can see it being introduced at extremely early levels of mathematics education, as early as the first few grades, to quash conceptual challenges with graphing equations before they have a chance to even become confusing.

Scott