Bunco and MATLAB (Module 4, ISTE-SS 5)

“One,” they say in approximate unison.
“One.”
“One. Two. Three. …Eight! Nine!”
“One. Two. BUNCO!!!” they scream, with a curious comradery considering they’re playing against each other.
“Nooo!” the other tables tease.
“What was your score? Sweet, I’m the loser!”

Once a month, my extended family gets together to play a game called Bunco. See here for some details; rules vary, and indeed our rules are a little different than what I linked. It’s a dice game. It might sound complicated, but I swear it’s incredibly easy. You take turns rolling and (in our rules) you want to be the first person to reach 21 points; there are specific point values associated with rolling certain things. At most Bunco parties we’ll play through the game six times. That’s a lot of dice rolling. It takes us about three hours. So one might eventually wonder, as I did, how many times, on average, does an individual need to roll to reach 21 points?

There is surely a mathematical solution to my question. You could also brute-force the answer by counting the number of times you had to roll to reach 21 points, over and over and over, and then averaging the results. That would take ages, but if you know how to play the game, you could do it. Or, with a little coding, you could have the computer brute-force the answer in no time at all! (Well, in 2 min and 27 sec, which actually felt like forever.)


This week’s module, Module 4, is about investigating ISTE Student Standard 5: Computational Thinker – “students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.” In response to Computational Thinker Indicator 5b, “students understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions,” I asked the investigation question:

What resources or programming tools are there that would be appropriate for students who have not previously done any programming? Maybe some good beginners tutorials for MATLAB, or something to teach the ideas used in programming (like vectors, for loops, if/else statements).

After poking around the internet and thinking about the setting of a college math class, I decided that I really did want to take this opportunity to look for a good beginner’s resource for MATLAB. MATLAB doesn’t have to be used as an advanced tool, and if you think of it as simply being a different (but epic) calculator, then I see no reason why beginning programmers shouldn’t be introduced to MATLAB. And furthermore, if you pursue math you’ll surely be introduced to it eventually.

MATLAB Resources

My two favorite resources that I found are:

Mikhelson’s video tutorials have the main things that I was looking for:

  • Zooming in on computer screen so you don’t have to squint.
  • Short-ish videos. I’m not really looking for entire hour-long, lecture-style lessons, just quick videos that give enough to know some basics.
  • Few enough videos, and covering the topics that I would want my students to know. Again, not looking for an entire course, I just want some good basics. The main topics I had in mind are: variable declaration, vectors, matrices, for loops, while loops, and if/else statements. But I like the other topics he included.
  • A slow enough speaking tempo.
  • Easy to follow visually.

I mostly just skimmed Xenophontos’ PDF, and I liked what I saw. It had a nice tone and layout. I found it easy to look at. Lots of good basics; more than the video tutorials, but not an exhaustive MATLAB manual. I think it could pair well with video tutorials as a reference.

Connecting MATLAB to ISTE Student Standard: Computational Thinker

Learning and using MATLAB easily touches on Computational Thinker Indicator 5b. For loops and while loops are two basic ways of programming the computer do repetitive tasks for so many iterations, or while some condition has yet to be met. When you write a script (a.k.a: code, program), you are writing a sequence of ordered steps. Coding in MATLAB or any other program is a manifestation of computational thinking.

But What Does This Have to do With Bunco?

Recall my game question: how many times, on average, does an individual need to roll to reach 21 points? This is a perfect question for MATLAB and I think a great example of using programming to answer a real-life question. The answer, by the way, is approximately 32.67 rolls. In order to program MATLAB to “roll the dice,” count how many times it took to reach 21, and then average the results, all I needed was: variable declaration, a vector, a for loop, a while loop, a few if/else statements, and two other commands – one to generate a random integer between 1 and 6, and one two average the number of rolls. Aside from the two other commands, all of these things are covered by Mikhelson’s tutorials in about 35 min.

It’s very freeing and rewarding to be able to answer your own questions, and a program like MATLAB opens you up to a new set of questions you can answer. It gives students a tool they can leverage while being a computational thinker. In addition to answering real questions, another reason a program like MATLAB is great tool to have at your disposal is because of what processes it can automate for you. For example, one time I was creating tons of bar graphs, which required calculating dozens and dozens of percentages. The tediousness and repetition of the task was making me cry on the inside. In comes MATLAB to save the day! Write a little code; copy and paste some tables; change a few numbers every now and then. Bam! Tables complete. I wanted to cry tears of joy over how much time MATLAB had saved me.

When I read Computational Thinker Indicator 5b, “students understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions,” the first thing I think of is MATLAB. It is a tool that enables you to embody this indicator. And as much as MATLAB can do, knowing even just a few basics can add such a powerful tool to your technology-toolbox. It’s a tool I want people, and my future students, to have access to.

(By access I meant the knowledge to use it, but speaking of access, Octave is the free “equivalent” to MATLAB; nearly all of its commands are identical. And typically, colleges will give students a discount on MATLAB and/or have MATLAB available for use on the school computers.)


References

ISTE: International Society for Technology in Education. (2016). ISTE standards for students. Retrieved from https://www.iste.org/standards/standards/for-students-2016

GNU Octave. (2017). Retrieved from https://www.gnu.org/software/octave/

MathWorks. (2017). MATLAB. Retrieved from https://www.mathworks.com/products/matlab.html?s_tid=hp_products_matlab

Mikhelson, I. (2014, March). MATLAB tutorials. Retrieved from https://www.youtube.com/playlist?list=PL1ec5YBm_crwcmeR8pKB9shvnriE8UbFE

Xenophontos, C. A beginner’s guide to MATLAB. Department of Mathematical Science, Loyola College. Retrieved from http://www.academia.edu/25726211/A_Beginners_Guide_to_MATLAB

Forums, curation, and mathematics (Module 2, ISTE-SS 3)

Module 2 is about investigating ISTE Student Standard 3: Knowledge Constructor – “students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.” Looking at the indicators generated a lot of questions for me about how I can foster these things in a college math class. I want to document all of my questions here for future reference, but I really investigated just two of them (in red text).

In response to indicator 3a, “students plan and employ effective research strategies to locate information and other resources for their intellectual or creative pursuits,” I asked:

In physics education research, there is a need to study how students use their textbooks (Docktor & Mestre, 2014, p. 22) and while there are some research-based textbooks, most courses do not use them (p. 21). So I’m curious if there is research on how math students use their textbooks. Are there any research-based math textbooks? What resources do students use when they have math questions – what do they do when they are stuck – what strategies do they use to get unstuck?

In response to indicator 3c, “students curate [i.e., to gather, select and categorize resources into themes in ways that are coherent and shareable] information from digital resources using a variety of tools and methods to create collections of artifacts that demonstrate meaningful connections or conclusions,” I asked:

Can I find a place where students are sharing resources in a coherent way? (Places to look: Reddit – YouTube – FB groups.) Can my website host a forum for students to share their resources? Can I use Facebook groups as part of the course? Can I require college students to participate in a FB group? (Should I?)

In response to indicator 3d, “students build knowledge by actively exploring real-world issues and problems, developing ideas and theories and pursuing answers and solutions,” I asked

I would like to see some examples of students exploring real-world issues in math. Can I find some real-world-related final projects? Or can I find some examples of inquiry-based math?


I decided to look into creating a forum on my website and using Facebook groups in college courses because I wanted to make sure I could offer my students a space for sharing class-related things with each other (and I’m not a huge fan of the LMSs that I’ve used – as a student – when it comes to sharing resources and communicating).

Question: Can my website host a forum for students to share their resources?

Yes.

WordPress has a variety of plugins for this. I installed “Forum – wpForo” (more information about the plugin can be found on their website, here). I am fairly happy with the forum. It has the main thing I want, which is threaded comments. Implementing the threaded comments theme was a little confusing (directions below), but otherwise installation was very easy. There are a few things I don’t love about the layout/display of the forums. For example, if you choose to “Answer” a post, you will add a normal comment, if you choose to “Add comment” you will reply in a threaded fashion – I wish they were called “comment” and “reply.” But overall, I’m pretty happy with the plugin.

(Version 1.1.1) To implement the threaded comments theme go to: Dashboard side panel > Forums > Forums > (click edit on the blue category) > (in the upper, right-hand box choose the “QA” category layout).

Question: Can I use Facebook groups as part of a college course? Can I require students to participate in a FB group? (But should I?)

Yes. Yes. And…no?

I’m sure it depends on the college, but from the looks of it, generally you can use FB groups in college courses, and it looks like some instructors do require FB participation. I found a great blog by Nisha Malhotra, PhD where she reflects on implementing FB in her course. The comments on the blog are also very insightful and show differing opinions on whether or not you should require FB participation.

Considering this blog was posted four years ago, I would like to find a similar resource but more current. A lot has changed in four years and I have a feeling students’ feelings about FB have changed. Indeed, it was just this last year that I heard for the first time, from a high school student, that FB is for old people! Who knew?! I would bet there are more people consciously abstaining from FB today than there were four years ago. (Not just because it’s “for old people,” but probably because of that too.)

While I really like the idea of a FB group for a class, I don’t think I could bring myself to require FB participation in a course. Based what I think FB can mean in our culture today, I think it is important to respect a student’s choice to not use FB. This is one reason I really wanted to look into putting a forum on my website. Then I could offer both as an option for online participation.

But is this really curation, or is it just collection?

By the end of this module, I decided that what I have really done is found resources that aid in sharing curations, rather than resources for curating. A classmate of mine found a wonderful blog about curating by Saga Briggs. I think Briggs paints a clear picture of what curation looks like and I now imagine curation as being able to say, “Here are some resources that I think are valuable, and here’s why I think they’re valuable together.” A forum or a FB group could be used in that way, but I think it would require prompting if the goal was to have every student curate resources. Additionally, Briggs includes a list of 20 resources for curating.

Possible Curation Assignment for Math

A while back I wrote a possible prompt that is more in line with collection. It needs to be adjusted to align with curation.

Initial prompt: Find a resource that helps you with something related to the course. Maybe identify something you struggle with and find a resource for that. Or maybe find a resource that helped you understand a topic better or helped you with a homework problem. Write a summary explaining what the resource is with the idea that you are helping someone decide if the resource would be valuable to them. Be sure to reflect on why it was helpful to you.

To turn this into a curation project, they could either share multiple resources that helped them with something and include in the summary why the resources are helpful together; or they could find additional resources after the fact to go with their “personally helpful resource.” The goal would be to create a “resource bundle” to help someone else with the same thing/topic/problem they needed help with. They could share this bundle to my forum or in a FB group.

I anticipate needing to help students learn how to find resources, but I also hope that they can learn from each other, and that this assignment could help them do that. O’Connor and Sharkey (2013) and Kingsley and Tancock (2014) both discuss how students struggle to find information when it requires digging, and during much of my undergrad that was definitely true for me. Somewhere in the beginning to middle of undergrad, I realized how unskilled I was at searching for information and using my textbooks. I realized this because I saw how my close friends/peers used their resources. They didn’t actively teach me how to do the same, but I began learning how to use my resources by watching them. I know what it’s like to not know how to search for information, and I know how valuable the skill is when you can.

Moving forward, I would like to check out the resources listed in Briggs’ blog and practice using them to get a better feel for the process of curating (as opposed to collecting).


References

Briggs, S. (2016). Teaching content curation and 20 resources to help you do it [blog]. Retrieved from http://www.opencolleges.edu.au/informed/features/content-curation-20-resources/

Docktor, J. L., & Mestre, J. P. (2014). Synthesis of discipline-based education research in physics. Physical Review Special Topics-Physics Education Research, 10(2), 020119, 1-58.

ISTE: International Society for Technology in Education. (2016). ISTE standards for students. Retrieved from https://www.iste.org/standards/standards/for-students-2016

Kingsley, T., & Tancock, S. (2014). Internet inquiry. The Reading Teacher, 67(5), 389-399.

Malhotra, N. (2013). Experimenting with Facebook in the college classroom. Retrieved from http://www.facultyfocus.com/articles/teaching-with-technology-articles/experimenting-with-facebook-in-the-college-classroom/

O’Connor, L., & Sharkey, J. (2013). Establishing twenty-first-century information fluency. Reference & User Services Quarterly, 53(1), 33–39.

wpForo. (2016). WordPress forum plugin. Retrieved from http://wpforo.com/

Sanity checking in mathematics (EDTC 6102 Module 1, ISTE-SS 1)

Update 5/14/18: I am looking for a different name for the idea of a “sanity check.” Currently, my favorite synonym is “plausibility check.”


For this module we are investigating ISTE Student Standard 1: Empowered Learner – “students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.” In response to Empowered Learner Indicator 1c, “students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways,” I asked the investigation questions:

What are some methods for sanity checking in mathematics, examples of a time when it was needed, and how do you teach this skill? How can students demonstrate sanity checking?

My own working definition of sanity checking is: the act of using tools, techniques, and information to answer the question “Does this even make sense?” This definition is very general and not math specific, though I will focus on its application in math. Sanity checking can be used while solving problems, or problem solving, and to check a final answer.

I felt sanity checking was related to ISTE 1: Empowered Learner because when a student spontaneously sanity checks their own work, they are taking an active role in their learning and they are seeking some type of feedback to inform what they are doing. Tools such as calculators, mathematics software, and Wolfram Alpha can be creatively utilized to get feedback/aid in sanity checking, and of course there’s always Google. I figure that while they may have not articulated their own learning goals, they are implicitly demonstrating an achievement-related goal, whether it’s to achieve sense-making or achieve the right answer.

In my experience, sanity checking was not something that was ever explicitly taught, in spite of its value as a skill and way of thinking. This led me to wonder what kinds of educational tools and research exist related to teaching sanity checking. To my surprise, I found exactly zero published journal articles related to the combined key words “sanity checking” and “mathematics education” (and related searches, like “sanity testing”). This makes me wonder if sanity checking goes by different name in research. Turning to Google, I found a few websites and books with some relevant information.

Q: What are some methods for sanity checking in mathematics?

Finding a list of methods was more challenging than I imagined. But from a few resources, I have put together the start of a list:

  • Estimation: For example, you can use estimation to check that an answer is reasonable (Petrilli, 2014).
  • Plug in numbers: If two things should be equal, are they in fact equal when you plug in a random number (Wood, 2015)?
  • Comparing against external information: Suppose you know that a penny weighs about 3 grams, and you calculate that an adult weighs 6 grams (i.e., two pennies). Compared to the external information, this answer does not seems reasonable. Wood (2015) and Yaqoob (2011, p. 33) mention related things.
  • Do the units make sense? (Wood, 2015) or Dimensional analysis: If you’re calculating a velocity (meters/second), but end up with kilograms*meters/second, something went wrong. More generally, you can often use the “fundamental dimension” like length, time, and mass instead of meters, seconds, and kilograms to sanity check.
  • Definition/rule/fact based: For example, checking that the hypotenuse is the longest side of a right triangle, since it always is. Fenner (2013) gives many examples of this kind of sanity checking.
Q: What are some examples of a time when it was needed?

We have to show students that sanity checking can be a meaningful activity but I did not find any information on how to do this. So I would love to know some real examples of when sanity checking was needed or valuable. More specifically, I would love to know about the experiences students have had where they found value in sanity checking. Perhaps this could be an interesting assignment – have them turn in a reflection at some point throughout the quarter explaining a time when sanity checking helped them while working on the coursework.

Qs: How do you teach this skill? How can students demonstrate sanity checking?

I did not find any information on these questions either. Of course, demonstrating real-time sanity checking while working with students can help teach the skill by exposure. Additionally, let students see your “backstage performance” (Olitsky, 2007) to show them the struggles you have and how sanity checking is helping you.

One of the difficulties with demonstrating sanity checking is that sometimes it leads you along a messy path. You might erase little things here and there. You might scrap the whole page and start over. I’m not sure that turning in a homework set including all those changes would be easy or very valuable (maybe it would), but this is one reason I like the idea of a reflection assignment that has them explain one meaningful sanity checking experience from the quarter. I will also keep thinking about ways that students could utilize technology to share their sanity checking stories or resources with each other.

Moving Forward

Sanity checking is a valuable skill in mathematics, and teaching sanity checking can help students become self-directed learners, which Kivunja (2014) considers to be an important 21st century skill. Considering the value of sanity checking, I would like to find some more resources on the topic, for example best practices to teach it or how students utilize sanity checking. I will keep my eyes out for synonyms that might lead me to the vein of research on this topic, and if none exists, then perhaps this is something I would like to research in the future.


References

Fenner, S. A. (2013). Basic mathematics for engineers (8th Ed.). Lulu Press, Inc. (link)

ISTE: International Society for Technology in Education. (2016). 1: Empowered learner. ISTE standards for students. Retrieved from https://www.iste.org/standards/standards/for-students-2016

Kivunja, C. (2014). Teaching students to learn and to work well with 21st century skills: Unpacking the career and life skills domain of the new learning paradigm. International Journal of Higher Education, 4(1), p1. Retrieved from http://files.eric.ed.gov/fulltext/EJ1060566.pdf

Olitsky, S. (2007). Facilitating identity formation, group membership, and learning in science classrooms: What can be learned from out‐of‐field teaching in an urban school? Science Education, 91(2), 201-221.

Petrilli, M. J. (2014). The Common Core sanity check of the day: Estimation is not a fuzzy math skill. Retrieved from https://edexcellence.net/commentary/education-gadfly-daily/flypaper/the-common-core-sanity-check-of-the-day-estimation-is-not

Wood, B. (2015). Sanity checking. Retrieved from http://mathmisery.com/wp/2015/04/06/sanity-checking/

Yaqoob, T. (2011). What can I do to help my child with math when I don’t know any myself? Baltimore, MD: New Earth Labs. (link)

Homework solutions, digital citizenship, and math education (EDTC 6101, Digital readiness project)

It stretches my thinking to imagine how Ribble’s (2013) nine elements of digital citizenship can be meaningfully incorporated into math education. Digital citizenship is a concept that relates respecting, educating, and protecting yourself and others while in an online world through nine elements: digital etiquette, digital access, digital law, digital communication, digital literacy, digital commerce, digital rights and responsibility, digital safety, and digital health and welfare. Technology is a large part of our culture and I believe that being a thoughtful digital citizen is as important as being a thoughtful citizen of the physical world, so I think it is important to teach digital citizenship where applicable. In my day to day life, digital citizenship feels like a highly relevant and core skill. However, during my math classes as an undergrad, I don’t feel like digital citizenship was ever addressed.

Pre-interview preparation

Since I was struggling to think of ways in which digital citizenship could be taught within a math class, I wanted to use the interview portion of EDU 6101’s Digital Readiness Project as a way to uncover some of the inherent connections. Therefore, I developed a list of questions based on the ways I thought technology could intersect with math education – including topics like gender-related differences in calculator/math software use, and accepting students as friends on Facebook – but I left the interview open enough to follow unexpected connections. For this project I interviewed math professor Dr. James Lambers of University of Southern Mississippi.

Post-interview infographic

This infographic represents some general information about technology and math education. What I chose to include was based on my interview with Dr. Lambers.

 

Post-interview reflection

Upon reflecting about the interview, one connection between digital citizenship and math education stood out to me as the most meaningful, and that is the connection to digital law with digitally accessible homework solutions. The connection is possibly more in spirit than technically an issue of copyright law, but the issue of students using digital homework solutions is morally and ethically similar to the problem of stealing content since both are an issue of presenting unoriginal work as your own.

As math educators, we want students to take ownership of their learning, and digitally obtained homework solutions via resources like Wolfram Alpha, Chegg, or past students can exacerbate the problem of students working to “get the grade” instead of working to learn. I don’t mean to say that using solutions is always negative for the learning process – it’s how solutions are used that makes the difference. I’m specifically referring to when students copy solutions without understanding what they’re copying, and this is the kind of behavior we want to prevent. I’m envisioning a connection where helping students develop their moral and ethical thinking for citing sources of digitally or otherwise obtained solutions could promote a shift from focusing on “getting the answer” to being responsible for the learning process.

James (2014) gives us some insight that may be useful for understanding students’ moral and ethical considerations regarding instructor-developed homework problems and solutions. Her research suggests that knowing the content creator can increase young people’s moral and ethical sensitivity (p. 63), and one study showed that students were more likely to use digital content without permission as opposed to physical content (p. 67). This makes me wonder if students may be more likely to respect a teacher’s request to not distribute solutions simply because the students know the teacher, and if the students may be more likely to not distribute physical handouts of solutions, as opposed to electronic solutions. Furthermore, her work suggests that young people who have created content within a community feel more responsibility towards that community and are more likely to employ moral and ethical considerations. This makes me wonder if developing a sense of community in a math class where students are also content creators could support their moral and ethical thinking about copying and distributing homework solutions.

Beyond the direct parallels made between James’ work and math education, these questions also got me asking broader questions about using solutions: How can we utilize James’ research to help us teach moral and ethical use? How are students thinking about the use of digital homework solutions? Are they making consequence-based decisions or employing moral and ethical thinking? When do they employ moral and ethical thinking? What activities increase the moral and ethical thinking of math students? Do they have a free-for-all mindset regarding solutions (p. 56)? These questions are very interesting to me and could inform possible directions for future dissertation work.

 


References

James, C., & Jenkins, H. (2014). Disconnected: Youth, new media, and the ethics gap. Cambridge, MA: MIT Press.

Lyublinskaya, I., & Tournaki, N. (2011). The effect of teaching and learning with Texas Instruments handheld devices on student achievement in algebra. Journal of Computers in Mathematics and Science Teaching30(1), 5-35. Retrieved from http://eric.ed.gov/?id=EJ924358

Munger, G. F., & Loyd, B. H. (1989). Gender and attitudes toward computers and calculators: Their relationship to math performance. Journal of Educational Computing Research5(2), 167-177. http://dx.doi.org/10.2190/R1HL-LG9J-1YN5-AQ4N

Program for International Student Assessment (PISA). (2016). Mathematics literacy: Gender. Retrieved from https://nces.ed.gov/surveys/pisa/pisa2015/pisa2015highlights_5c.asp

Ribble, M., & Miller, T. N. (2013). Educational leadership in an online world: Connecting students to technology responsibly, safely, and ethically. Journal of asynchronous learning networks, 17(1), 137-145. Retrieved from http://eric.ed.gov/?id=EJ1011379

Svadilfari, Sean. (2008). Homework. Retrieved from https://www.flickr.com/photos/22280677@N07/2272656387