What can I do right now? (Module 5, ISTE-TS 5; and ISTE-CS 6)

So for this week, we are wrapping up by investigating ISTE-TS 5: Engage in professional growth and leadership – “teachers continuously improve their professional practice, model lifelong learning, and exhibit leadership in their school and professional community by promoting and demonstrating the effective use of digital tools and resources” which is closely related to ISTE Coaching Standard 6: Content knowledge and professional growth – “technology coaches demonstrate professional knowledge, skills, and dispositions in content, pedagogical, and technological areas as well as adult learning and leadership and are continuously deepening their knowledge and expertise.” Since I’m not currently teaching, for this module I wanted to investigate:

What I can do right now to engage in ISTE-TS 5 and ISTE-CS 6?

Micro-certification (or an informal list)

One of my colleagues in my cohort, Karen, has mentioned micro-credentialing as a way for teachers in a school communicate to each other what technologies they have proficiency in; this would help teachers know who they can go to for help with, or ideas for, using certain technologies. (Here’s a link to her blog.) This inspired me to make a list of technologies I feel I feel I could offer some assistance with on my About page. I’m not certified in any of these tools, but I think it would be a nice practice to keep an informal list posted as a sort of beacon: “Hey! I’m willing to help and have some knowledge about using these things.” One of my goals in doing this is to offer a way to professionally connect and to offer an open hand to the community around me.

Karen also shared with me the Google Educator Certification that you can do. This training leads to certification in using Google tools in the classroom. I got started with it to check it out. The training portion is free, and then the test for certification costs $10 (for Level 1 that is; Level 2 costs $25). There are 13 units in the training, so not something I could do in one sitting. Since I’m not going to be teaching for a few more years still, I think it would be wise to wait on completing the certification as a lot can change in three years.

Swimming through honey

ISTE-CS 6 says I should demonstrate my professional disposition in pedagogical areas, and one of the things I believe in is asking humans questions and asking humans for help and support. If I take the trend of self-teaching via the Internet to the extreme (a common practice in physics), we would never ask each other for assistance, because “you can Google it.” I see this expectation happening in small ways all the time. And there is merit to expecting someone to Google something instead of asking, especially if in order to answer their question, you have to Google it yourself. But sometimes you really just need to ask a person. Sometimes you just want that – sometimes I want that.

I consider myself quite good at seeking out information online (wow, am I actually saying that? Six years ago I was terrible at it), but sometimes I just want to talk to a human. Sometimes you need a dynamic conversation that you can take in a new direction at any moment. “Wait, what does that mean? Can you say that in a different way? How does that connect back to what you said before?” Sometimes self-teaching feels like swimming through honey (i.e. it takes a lot of effort), and I believe in accompanying people to the lake instead, when you can (i.e., it’s still work, but a good deal easier).

I want to reiterate, self-teaching is a necessary skill and I do expect that people engage in that activity. But in today’s culture, and in my experience, I often feel the need to advocate for that human-human, teaching-learning interaction, and that’s what I’m trying to do by putting up the “I’m will to help with these things!” beacon.

Reflecting

These standards really encouraged me to reflect on the changes I’ve experienced since joining the DEL program in September. When I started this program, I had a very fuzzy idea of what “technology in education” means and is. I felt like the word “technology” just got thrown around in mission statements and course objectives (I’m thinking about my time in undergrad), and I never really got the point.

Over the last three quarters, my thinking and understanding has changed. I don’t know if I have the words to tell you how yet, but I do see things I didn’t see before. Indicator 5b says “exhibit leadership by demonstrating a vision of technology infusion…” and those words make sense to me now. I have a version of this poster on my wall, and now the words mean something to me rather than just being a collection of buzzwords.

ISTE’s free classroom poster (click the image to go to the link)

I really have learned so much about living with technology in general, and about incorporating technology into education. When I started this program, the only ways I knew how to link technology and math were through calculators, mathematics software, and clickers. Now I can see ways to use screen capturing (OBS Studio), citation software (Mendeley), animations (PowToon), online whiteboards (Ziteboard), digital graphics tablets (Huion H420), and communication platforms (Slack), among other things. I feel ready, in a way I didn’t before, to think about how I can do ISTE-TS 5 and be a leader in educational technology.

Now, as I move forward, I need to start finding ways to engage in that leadership that I have a clearer vision for. In the coming months, I’d like to find a instance or two where I can offer someone some sort of guidance in finding or using a tool to suit their needs.


References

ISTE: International Society for Technology in Education. (2016). Free classroom poster: I am a digital age learner. Retrieved from https://www.iste.org/explore/articleDetail?articleid=843&category=Set-the-standard&article=

ISTE: International Society for Technology in Education. (2017). ISTE standards for coaches (2011). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Digital citizenship clicker questions in math, and Mendeley (Module 4, ISTE-TS 4)

This week we are looking at ISTE-TS 4: Promote and model digital citizenship and responsibility – “teachers understand local and global societal issues and responsibilities in an evolving digital culture and exhibit legal and ethical behavior in their professional practices.” In past blog posts I have discussed ways in which digital citizenship is or can be particularly relevant to a college math class – see my Mission StatementDigital Readiness Project, and Backwards Design Project. From these past…”musings” as I want to call them, what emerged as one of the most pertinent ways to tie in digital citizenship is the ethical use of digital tools to help students do their math homework – I mostly talk about that in the Digital Readiness Project. Another major thought I’ve had is that if you want to teach digital culture in relevant way, integrating online spaces for collaboration into the structure of the course helps – I mostly talk about that in the Backwards Design Project.

So for this module, I was hoping to find an example of a lesson plan or some thoughts on how to digital citizenship in a math class; an example of a teaching doing Indicator 4a – “advocate, model, and teach safe, legal, and ethical use of digital information and technology, including respect for copyright, intellectual property, and the appropriate documentation of sources” – in the context of math. My investigation questions were:

When teaching digital citizenship in a college math class, what can implementation look like/how can you implement it? Can I find any example lesson plans?

Clicker Questions on Ethics

I didn’t find what I was looking for in the context of a math class, but I did find a great blog post by Derek Bruff (2010), Ethical or Not? Clicker Questions about Academic Integrity. In this post, Derek shares the clicker questions he asked his writing students (which were written by himself and a colleague, Maggie Bowers) and talks about the students’ responses/the discussion around these questions. The post is very insightful and offers a glimpse into the classroom during the lesson. (For day two of Derek’s lesson with more clicker questions, check out his other blog here. For a description of clicker questions, check out his guest blog post on Busynessgirl’s blog here.)

Since I didn’t find anything like this for math, and his questions did stimulate an engaged discussion around ethics, I thought I would try using his questions to inspire my own. I’m just brainstorming here and would call this a draft. But it’s a start! Some of Derek’s questions would be relevant to a math class, so I did include them below – 4, 5, and 6. And not all of these questions have a digital component, which I will say more about in a moment.

  1. You are stumped by a homework problem, so you…
    1. use Wolfram Alpha to look up the solution. Ethical or unethical?
    2. get help from someone. They write out a solution and it makes sense to you, so you rewrite the solution and turn it in. Ethical or unethical?
  2. You are working with a friend on a homework assignment. The two of you collaborate to write a solution on a whiteboard. Both of you rewrite the same solution for your homework. Ethical or unethical?
  3. A friend of yours took this course last quarter and gives you…
    1. pictures of their homework from the class so you can check your work. Ethical or unethical?
    2. pictures of their old exams from the class so you can study for your exams. Ethical or unethical?
  4. The student next to you drops his test and you accidentally see the answers. This leads you to change one of your answers. Ethical or unethical? (Bruff and Bowers, 2009)
  5. You get a B- on an exam. You would really like a B, so you ask your professor after class for a few extra points on a particular exam question, even though you know your answer probably doesn’t deserve a higher score. Ethical or unethical? (Bruff and Bowers, 2009)
  6. You find a copy of the instructor’s solutions manual to one of your textbooks online. You use it to check your homework before turning your homework in. Ethical or unethical? (Bruff and Bowers, 2009)

Like I said, some of these don’t have a digital component, like 1.2 and 2 – however they could if you add in taking photo of the work. And similarly, the 3 doesn’t need to involve pictures to get at the same underlying ethical question – maybe your friend gives you the hard copies of their work. So if I were to develop these questions further, I would want to be more thoughtful about how I include technology in the questions, because it’s not always true that the heart of the ethical dilemma is inherently tied to technology. Instead, with some situations, it’s simply that digital tools make it easier to perform certain actions.

Imagining that I were to use these or similar questions, as part of this discussion I think it would be important to clearly define plagiarism in the context of a math class.

Now let’s abruptly switch gears…


Mendeley for Citation Generation and Management

On a different note, I found a free tool that is helpful for generating citations and references within Word: Mendeley. Citing our sources is important for students and teachers alike. In regards to ISTE-T4, Mendeley could aid teachers in doing Indicator 4a (i.e. modeling good citation practices) by making it a little easier to cite your sources – particularly if you are citing the same things more than once.

Mendeley is a free citation management tool. It has extensions for Word and most Internet browsers. In Word, it assists you in doing in-text citations, and will generate and update a references list. Online, it detects citation information so that you can add a citation to Mendeley while browsing, and whatever information it doesn’t detect, you can add. Here is a quick demonstration. (Looks like I need to figure out some better OBS Studio settings to make the image clearer!)

There is a WordPress plugin…but I couldn’t figure out how to use it. Nevertheless, if you’re in Word, this is a great tool and I can’t believe I only just started using it!


References

Bruff, D. (2010). Ethical or not? Clicker questions about academic integrity [Blog post]. Retrieved from http://derekbruff.org/?p=799

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Mendeley. (2017). Retrieved from https://www.mendeley.com/

Screen capturing (Module 3, ISTE-TS 3)

This week we are looking at ISTE-TS 3: Model digital age work and learning – “teachers exhibit knowledge, skills, and work processes representative of an innovative professional in a global and digital society.” Looking at TS 3 and its indicators, I asked:

What is a digital tool math teachers could use to achieve one or all of these indicators?

While pondering this, it occurred to me that a screen capture tool (aka screencasting or video capture) would be great for this standard. I actually began my investigation of screen capturing last quarter, betting that it would be relevant to the ISTE-TSs at some point. Sure enough, Indicator 3c just screams “screen capture!” to me – “communicate relevant information and ideas effectively to students, parents, and peers using a variety of digital age media and formats.” Here’s why, in a semi-VLOG-like style, while screen capturing:

My Resource – OBS Studio

The screen capture tool I went with is OBS Studio. I searched around and found that OBS Studio was the most frequently and highly recommended free screen capturing program. As I understand it, OBS is is often used by gamers to stream their game-play, and there are tons of tutorials on YouTube about how to use OBS Studio.

A tutorial I found super valuable was OBS Studio Tutorial: Studio Mode by WDA_Punisher. After a few weeks of sporadic use, I had not been able to figure out how to use Studio Mode on my own, so I looked it up. Indeed, it is a valuable feature within OBS Studio to help make your videos cleaner and more professional looking as you transition between the windows that you want to capture. However, it is not a necessary feature to get started with basic screen capturing.

To give you an idea of what OBS Studio looks like, I made a demonstration video using OBS Studio. (Note: I am not adding sources from scratch, so the first time you go through this process it will look a little different. Sorry about that.)

In a Math Class

The ways I immediately see a screen capturing tool as being helpful in a math class include: demonstrating how to use the class LMS or online homework system, or answering student questions outside of class. I’m envisioning screen capturing while using the drawing tablet I recently blogged about (here) to perhaps answer some student questions outside of class.

An aside: Speaking of screen capturing and using my tablet, can I take a moment to plug my Global Collaboration Project for this quarter? I’m collecting, curating, and sharing stories of times math was useful. I’ve gotten fantastic responses and I look forward to blogging about it! (Here are more details and the form to submit a story if you’re interested.) For one of my own story submissions, I used OSB Studio, my Huion H420 tablet, and OneNote to screencast a part of my story! (Video here, full story here.)

Earlier I highlighted Indicator 3c in relation to screen capturing because it works so well to enhance communication in those situations where you need to communicate online, but wish you could show the person your computer screen too. But the situations that may come up where you want to show a colleague or student, or someone else, what you see on your computer are endless. I’m sure there are situations where you could use screen capturing to: “demonstrate…the transfer of current knowledge to new technologies” (Indicator 3a), “collaborate with students, peers, parents, and community members…to support student success and innovation” (Indicator 3b), or “model and facilitate effective use of current and emerging digital tools to locate, analyze, evaluate, and use information resources to support research and learning” (Indicator 3d).

In general, screen capturing is just a good tool to have in your tool bag, ready to use when you need it. And I do recommend OBS Studio. It has been a great free program so far!


References

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Open Broadcaster Software. (2017) OBS Studio. Retrieved from https://obsproject.com/

WDA_Punisher. (2016, March) OBS Studio tutorial: Studio Mode. Retrieved from https://www.youtube.com/watch?v=5xFA4zCIptA

Peer Instruction-like resources for math (Module 2, ISTE-TS 2)

One of my most memorable college experiences as a student involved the use of clicker questions, but used in a little bit of a non-traditional way. The class was “baby quantum” as we called it. It was a prerequisite for the intro quantum mechanics sequence.

Typically, in my experience as a student, a multiple-choice question is presented on the projector, the students talk about it for 2ish minutes, we each submit our answer by pressing a button on our own clicker device, the final results are displayed as a histogram, and then we wrap up by talking about the answer options as a class.

On this day, however, we were not allowed to consult one another. Instead, we silently answered the question, we were not shown the final histogram, and we did not follow up by talking about the question/answer. We then switched gears and worked together on related a UW Tutorial. After we completed the tutorial, we were presented with the same clicker question again, giving us the opportunity to change our answer (I don’t remember if we were allowed to talk to each other this time – I would guess not). And again, we were not yet shown the results. But we could tell by the instructor’s reaction that something interesting had happened. She then revealed the histograms…

First she showed us the histogram from round one – I don’t remember the distribution off the top of my head, but it was more or less all over the place. Then she showed us the histogram from round two. The gasp was audible and there was a mild uproar – over 90% of us now chose the same answer! The right answer.

It’s hard to describe how exciting it was, and the story is also a success story about the tutorial we were working on (see here for a journal article on the tutorial, which includes the actual clicker question stats from this day). But we were elated. There was such a stark contrast between the histograms. The use of clicker questions really showcased the power of the tutorial. From an instructor’s perspective, the tutorial is probably main point of interest, but for me, the final reveal of the clicker question results is really what that made that day so memorable. Our jaws dropped to the floor.


For Module 2 we are looking at ISTE-TS 2: Design and develop digital age learning experiences and assessments – “teachers design, develop, and evaluate authentic learning experiences and assessments incorporating contemporary tools and resources to maximize content learning in context and to develop the knowledge, skills, and attitudes identified in the Standards•S.”

In particular, two indicators stood out to me as related to the use of clicker questions/classroom voting systems (CVS): Indicator 2a – “design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity,” and Indicator 2d – “provide students with multiple and varied formative and summative assessments aligned with content and technology standards, and use resulting data to inform learning and teaching.”

To go through the points in those indicators: Research has shown positive results on student learning with the use of CVS (Cline and Zullo, 2011; Crouch and Mazur, 2001). You can, but don’t have to, use digital tools to implement the questions. There is room to increase relevance by choosing questions that you feel your particular class needs to discuss. Discussing their answers with each other gives them more opportunity to think and reflect, and thus develop their own way of imaging the math (i.e., being mathematically creative). One of the main ideas behind CVS is to use the activity as a formative assessment. Additionally, students report that CVS are engaging, and from experience, I would agree.

I am familiar with physics related CVS resources. Peer Instruction (PI) by Eric Mazur (1997) details a particular methodology around the use of clicker questions and provides a set of physics clicker questions. In Henderson and Dancy’s (2009) study, they found that PI was the most commonly used research-based instructional strategies in college physics. So my question was (and has been for some time):

What are some PI-like resources for the college math class? Is there a bank of PI-like clicker questions for math?

To my surprise (although maybe I shouldn’t be surprised), I found exactly what I was looking for. The links below come from a Phoenix College page, Clicker Questions and Math, or from one of the pages it links.

What Are Clicker Questions?

For a more elaborate, yet still quick, overview of the process and benefits of using clickers, I will refer you to Derek Bruff’s guest blog post (2009), Teaching Math with Clickers, on busynessgirl’s blog. On his own site, Bruff’s posts (2009), Flexible Clicker Questions, details a particular time he asked a clicker question. The way Bruff describes using student-submitted “bucket questions” as clicker questions makes his clicker questions particularly relevant to his class. He also says that this gives him a better sense for how prevalent the confusion is, rather than just answering student-submitted questions at the start of class (i.e., it works as a relevant formative assessment).

For a lot of elaboration about CVS in math, check out editors Kelly Cline and Holly Zullo’s (2011) book, Teaching Mathematics with Classroom Voting: With and Without Clickers.

“This collection includes papers from faculty at institutions across the country, teaching a broad range of courses with classroom voting, including college algebra, precalculus, calculus, statistics, linear algebra, differential equations, and beyond. These faculty share their experiences and explain how they have used classroom voting to engage students, to provoke discussions, and to improve how they teach mathematics.

This volume should be of interest to anyone who wants to begin using classroom voting as well as people who are already using it but would like to know what others are doing. While the authors are primarily college-level faculty, many of the papers could also be of interest to high school mathematics teachers.” (Mathematical Association of America, 2017)

I haven’t read all of the book, but it seems valuable and I will likely purchase it. I thought chapter 2 offered an insightful breakdown of implementation options, addressing: clickers or non-electronic voting, one- or two-cycle voting, and to grade or not to grade the responses.

This book is generally geared toward college instruction, but I want to point out chapter 8, Using Clickers in Courses for Future K–8 Teachers, for my K-8 teacher friends.

Resources for Math Clicker Questions

So what about the CVS questions themselves? These two resources offer pages and pages of ready-to-use CVS questions for a variety of college math topics/courses. (Both projects were NSF funded.)

I worked through one of the Math QUEST question sets (The Fundamental Theorem and Interpretations set in the Integral Calculus question library) and I really liked it. I felt that the questions did a good job setting the stage for subsequent questions. Multiple times the next question touched on something I had just been thinking about. For example during question 7 I thought, “Well (a) would be right if it were |v(x)| instead of v(x),” and then question 8 asked about |v(x)|. So I was happy with the progression of the questions.

Last Thoughts

These resources are really exciting to me. Clickers are something that I really want to incorporate into my future teaching and it’s nice to finally tap into that vein of research. As easy to find as these resources were, I’m not quite sure why I haven’t found them already!


References

Bruff, D. (2009). Flexible clicker questions [Blog post]. Retrieved from http://derekbruff.org/?p=163

Bruff, D. (2009). Teaching math with clickers [Blog post]. Retrieved from http://busynessgirl.com/teaching-math-with-clickers/

Cline, K. S., & Zullo, H. (Eds.). (2011). Teaching mathematics with classroom voting: With and without clickers (No. 79). Mathematical Association of America (available here). Retrieved from http://ebookcentral.proquest.com/lib/spu/detail.action?docID=3330312

Crouch, C. H., & Mazur, E. (2001). Peer Instruction: Ten years of experience and results. American Journal of Physics, 69, 970-977.http://dx.doi.org/10.1119/1.1374249

Henderson, C., & Dancy, M. H. (2009). Impact of physics education research on the teaching of introductory quantitative physics in the United States. Physical Review ST Physics Education Research, 5(2), 1-9. https://doi.org/10.1103/PhysRevSTPER.5.020107

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Mathematical Association of America. (2017). Teaching mathematics with classroom voting: With and without clickers. Retrieved from http://www.maa.org/press/ebooks/teaching-mathematics-with-classroom-voting-with-and-without-clickers

Mazur, E. (1997). Peer instruction: A user’s manual. New Jersey: Prentice Hall, Inc.

Novak, G. (2006). What is Just-in-Time Teaching? Retrieved from http://jittdl.physics.iupui.edu/jitt/what.html

 

Imagining math (EDTC 6103 Module 1, ISTE-TS 1)

This quarter, we’re exploring the 2008 ISTE Teacher Standards (which I will be abbreviating ISTE-TS), and for module 1 we’re looking at ISTE-TS 1: Facilitate and inspire student learning and creativity – “teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity and innovation in both face-to-face and virtual environments.” What really stood out to me when reading through the standard and its indicators was the idea of creativity. Along with creativity being mentioned in the standard itself, two of the indicators mention it: Indicator 1a – “promote, support, and model creative and innovative thinking and inventiveness” and Indicator 1c – “promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative process.” This emphasis on creativity led me to ask:

What is mathematical creativity? What does the research say about how to conceptualize mathematical creativity, and how to identify and foster it in students?

A Treasure Trove of Conference Papers

I felt that I needed to know more about this before I could fully see ISTE-TS 1. While searching for answers, I immediately stumbled upon a fantastic webpage, The 11th International Congress on Mathematical Education, Discussion Group 9: Promoting Creativity for All Students in Mathematics Education. This webpage has about 40 conference papers that speak to one of the following questions:

1. What is mathematical creativity and which mathematics students can and should be creative?
2. What is the role of the teacher and others in recognizing and promoting mathematical creativity? What is the goal in doing this?
3. How might mathematical problems be used to develop mathematical creativity? How might mathematical creativity be assessed? How do we evaluate our success in developing mathematical creativity in all students?
4. How do technology, other resources, and the environment affect the mathematical creativity of the student?

I only scratched the surface of information this website has to offer, reading just two of the papers from question 1 above.

Aralas’ (2008) paper, Mathematical creativity and its connection with mathematical imagination, helped me pull the idea of imagination into the construct of mathematical creativity, and the word “imagination” struck a chord with me instantly. Being able to picture the math – or imagine the math – has always been really important to me, even if all I’m imagining is rearranging numbers with animation. But it’s a picture I strive to see. It’s a need really. I need to be able to see it. Picture it. Imagine it.

There’s a notion lurking around that goes something like, “The math that students are learning has already been discovered. It’s already done. Where’s the room for creativity and inventiveness?” I don’t exactly know why I feel like this notion is lurking around. It’s probably a collection of things I’ve heard or thought. But Mina’s (2008) paper, Promoting creativity for all students in mathematics education, helped me feel like I could settle into the idea that the math is new to the learner, and being mathematically creative isn’t necessarily about inventing new math, but also about the way we understand the math we are being taught.

Bringing Your Imagination to Life

With these two things in mind, I came to the conclusion that students can be mathematically creative in how they imagine the math they are learning. I am picturing a project where I ask students to show what they are imagining for whatever math idea they choose, through whatever way could best convey what they imagine.

To try and make it more clear what I mean, I did the activity myself. I wanted to try and show you what I imagine when I imagine the distance formula: d = x_{2} - x_{1}. I really wanted to make an animation because I imagine a moving-picture-like scene. I used PowToon to make my animation. (I’ve never used PowToon before, and I think it deserves its own investigation and blog post somewhere down the line – it was awesome, check it out!) My animation doesn’t perfectly depict how I imagine this, in the way that cartoons don’t perfectly depict 3D and real life, but it’s darn close! And it definitely represents what I really am imagining.

As a first time user of PowToon, this animation took me about 8 hours.

Of course, bringing to life what you imagine doesn’t have to be done through an animation. It could be a drawing, or a story, or something you build. It could be a demonstration. Maybe even a skit. I think one of the great things about asking students to show what they’re imagining, is that it would give them the opportunity to think about their toolbox of resources, and to search for the best way to bring their imagination to life (which is a rare in a college math class, in my experience).

Thinking in terms of my student-identity, creating this animation made me reflect on my mathematical idea and it pushed me to clarify my own thinking – there couldn’t be any fuzzy places in my mental movie. This didn’t have the collaborative element for me, but otherwise I felt like it hit strongly on ISTE-TS Indicator 1c.

With the way I’m thinking about this activity, it’s very important to focus on allowing students the space to convey their ideas, whether the ideas are canonically correct or not. I am not thinking that their imagination needs to be free of mathematical errors. However, what they create can be used to discuss any errors that emerge, or limitations to a way of thinking, but the point of the activity is not to create a “correct picture” – the point is to illustrate what they are thinking, whatever that may be.

I would love to assign this project one day and/or see what your students create if you decide to give this a try!


References

Aralas, D. (2008). Mathematical creativity and its connection with mathematical imagination. In Proceedings The 11th International Congress on Mathematical Education, Discussion Group 9: Promoting Creativity for All Students in Mathematics Education. Retrieved from http://dg.icme11.org/tsg/show/10#inner-documents

ISTE: International Society for Technology in Education. (2017). ISTE standards for teachers (2008). Retrieved from https://www.iste.org/standards/standards/standards-for-teachers

Ming, F. (2008). Promoting creativity for all students in mathematics education. In Proceedings The 11th International Congress on Mathematical Education, Discussion Group 9: Promoting Creativity for All Students in Mathematics Education. Retrieved from http://dg.icme11.org/tsg/show/10#inner-documents

PowToon. (2017). Retrieved from https://www.powtoon.com