This course will become read-only in the near future. Tell us at if that is a problem.

Hijack this thread!

This is our mini-forum for general conversations about the course. Got an idea? A question? Want to add thoughts to the past topic? Found a cool math video? Put it all here!

For my part, I am going to place recordings of the weekly meetings into comments to this thread. And probably some XKCD comics


Task Discussion

  • Gina Mulranen   April 17, 2013, 8:36 p.m.

    Here is the notes from the Computer Programming chat on 4/17/13:

    Moderator: Hello everyone! This is Gina. Dr. Droujkova could not be here tonight so I am using her access link to run the chat. So when you see her name, it is really me! =)

    Moderator (Katherine): hello!

    Moderator (Katherine): okay, I paused the video

    Moderator (Meagan): This is actually the video I found earlier for task 1  

    Moderator (Maria Droujkova): Great! I really like this one =)

    Moderator (LisaRittler): ok- paused   

    Moderator (LisaRittler): sounds good!

    Moderator (Maria Droujkova): Hello! We are currently watching the video.

    Moderator (Maria Droujkova): Thank you for coming!

    Moderator (Meagan): I already watched it so I am done whenever every one else is   

    Moderator (MariaD (really)): Hello! Glad things are working out. I actually have to run (I am in the middle of things), but I wanted to say Hi and to check. Carry on, I will catch the recording

    Moderator (Maria Droujkova): Okay. Thank you!

    Moderator (MariaD (really)): Hugs

    Moderator (Maria Droujkova): Please let me know when you are finished watching. Thank you!

    Moderator (Sue): I'm done!

    Moderator (LisaRittler): Im done too

    Moderator (Katherine): just finished

    Moderator (Maria Droujkova): Meagan - I was terrified of computer programming. I worked with java and I learned how to do programming with checkers and chess. Kids don't realize that their video games are computer programming and how many doors can be opened with learning it!

    Moderator (Maria Droujkova): Lisa - I loved the video! I was also terrified by computer programming but I now appreciate it and its problem solving aspects. I am 41 and I did not have contact with a computer until college. I used Pascal and it was over my head, but I do think that it should be on the middle school level.

    Moderator (Maria Droujkova): Katherine - My dad was a programmer and I grew up with it. I also took a computer programming class in college C++. I do not think I would see myself using it, but I can see how computer programming can teach how to break about problems.

    Moderator (Maria Droujkova): Sue - I learned computer programming in middle school as an elective. I did it for 2 years and did not pursue it in junior high. I worked with Basic and there was no interface. There was multiple processors that you wrote macros on. I also took Java in college. I do not see it as a career choice because I like working with children. But programming teaches you process and clear instruction. This is a very important skill.

    Moderator (LisaRittler): I can do that! take notes!

    Moderator (LisaRittler): I"m on it! I'll do my best!!

    Moderator (LisaRittler): Gina: Started in college in programming. Loved it! Very intimidating at first

    Moderator (LisaRittler): Gina: It was very "mathy"...created program that played baseball to play for World Series with Stats with probability. Learned "Scratch" when I starting working

    Moderator (LisaRittler): Gina: Students intro'd to me. Problem solving huge part of programming. ..breaking apart a bigger issue into smaller parts.

    Moderator (LisaRittler): Gina: What are benefits of teaching programming in middle school? Parents concerned to do this when the BASICS of Math are not mastered?...controversial...

    Moderator (Katherine): sorry!

    Moderator (LisaRittler): Gina; I can keep note taking now to...?

    Moderator (Maria Droujkova): I got it!

    Moderator (Maria Droujkova): Thank you!

    Moderator (Maria Droujkova): Meagan - I think middle school is a great time because some students have learned a lot of the skills over and over each year. We can incorporate programming into the skills they have already learned.

    Moderator (Maria Droujkova): Sue - Programming can make math interesting! And it also does not need to be math heavy. The students who are more advanced can have a colloborative learning environment. Teaching the importance of problem solving and attention to detail is important for everyone.

    Moderator (Meagan): Yep. 2 year old can unlock ipad and open netflix to watch Thomas!

    Moderator (Sue): hahaha

    Moderator (LisaRittler): Gina: collaborative learning environment will be set up in my class next week  

    Moderator (Maria Droujkova): Katherine - Starting early makes it easier to learn! My daughter is 5 and knows how to work a computer. There is not a learning curve like you would encounter teaching older students. Programming skills can enhance, not replace the skills.

    Moderator (Maria Droujkova): That is great Lisa! I love it!

    Moderator (Maria Droujkova): Lisa - Public schools need to focus on creating opportunities for important real-life skills. We need to be introducing these things so they are not foreign to them. Middle school should be where we start! This is where the future lies. Education is behind this curve and its frustrating. As a owner of a small business, I have to feel comfortable with technology. It held me back because I wasn't as well versed in it from an early age.

    Moderator (LisaRittler): Gina: we all made good points. Programming makes math interesting...Students very excited to "play around" with computers...they will gain experience!

    Moderator (LisaRittler): Gina: ideas start about what careers in middle school. ...gaining real life experience is so important.

    Moderator (LisaRittler): Gina: Computer programming...problem is the do we incorporate this? and still accomlish our required curriculum

    Moderator (Maria Droujkova): Sue - Making it mandatory to expose students to the possibilities they have. I encountered it in middle school and I thought it was great for that age group.

    Moderator (Maria Droujkova): Meagan - I don't know how to incorporate it. Start out with something small. One Scratch per marking period and then it could become a course on its own.

    Moderator (Maria Droujkova): Lisa - This is tough. As a parent and a teacher, you have to realize that your voice is important. If you students are interested, speak up! Speak to administers and advocate for the students. We can see this movement happening and it is important we colloborate with the students who will be our decision makers. Get a group together to make it effective.

    Moderator (LisaRittler): Congrats Katherine!!!!

    Moderator (Sue): congratlulations!

    Moderator (Meagan): Great!

    Moderator (LisaRittler): Sounds like the schools I've been in!

    Moderator (Maria Droujkova): Katherine - This is something I have been thinking about too because I just got a job. I am thinking about next year. There is not a single computer or projector. This will be a huge challenge. There is a computer room. I have will have a lot of freedom with the cirriculum so I am looking into ways to incorporate technology.

    Moderator (Maria Droujkova): Wow Katherine!

    Moderator (Maria Droujkova): Talk about a challenge!

    Moderator (Maria Droujkova): Go you!

    Moderator (Sue): Wow!

    Moderator (LisaRittler): the are a ton of grants out there from tech companies as well to try to get tech into classrooms!

    Moderator (Katherine): thank you!

    Moderator (LisaRittler): Bill Gates foundation..can't remember name

    Moderator (Katherine): I'm not sure where to start looking for grants, so if anyone has any resources I'd love advice!

    Moderator (LisaRittler): Gina: Katherine, you have quite a challenge... possibly look into grants...

    Moderator (LisaRittler): please put links on course to any grants for tech in classroom

    Moderator (LisaRittler): Gina: Give students option of using Scratch to complete math assignments

    Moderator (Meagan): Yep and my iphone

    Moderator (Katherine): my daughter learned how to unlock my iphone at 18 months!

    Moderator (LisaRittler): Gina: Its very important to get tech in classrooms bc really young even toddlers using computer.

    Moderator (Meagan): This helped me for this week. they are great lessons and easy to follow

    Moderator (LisaRittler): Gina: see web:

    Moderator (LisaRittler): Gina: give good tutorials on how to use Scratch. Nervous on how to teach kids to learn scratch without taking too much time in classroom. hoping students can use this website

    Moderator (LisaRittler): Gina: We can do it! Will be challenging...but students can use at their own pace and be able to apply it. Try to give homework...thats simple enough and not too time consuming and then create end of year programming project.

    Moderator (LisaRittler): Gina: 24 students signed up for elective starting next week.

    Moderator (LisaRittler): Gina: Any ideas on how to incorporate?

    Moderator (Meagan): no

    Moderator (Maria Droujkova): Lisa - Schools have very low technology and the technology we have is just sitting there or broken. Teachers are not out to learn it because they are busy. We should be giving students options so it can be looked at as a privledge to gain this knowledge. Also being able to share with their classmates is incredible.

    Moderator (LisaRittler): Gina: Tech is tough bc it doesnt always work...must have back up plans... plan for trouble shooting. This is why it probably hasnt caught on bc so many aspects are scary from parents and troubleshooting. some of us are scared bc we're no experts

    Moderator (LisaRittler): Gina: Students more advanced...but want to jump right into it...THIS IS LEARNING FOR EVERyone  

    Moderator (LisaRittler): Gina: Growing together. Technology ...we ned to catch up with it. Students may have different take on learning and thinking of it more collaboratively ...give whole new spin

    Moderator (Maria Droujkova): Katherine - Learning is not something that starts and ends. It is a lifelong process and involves taking risks. It is important for the students to task risks and for teachers to model that by taking risks. You get better by practicing. When they see the teaching learning, they are reminded that learning is lifelong. Seeing that as an experience is so valuable.

    Moderator (Sue): I agree!

    Moderator (LisaRittler): Gina: Thank you... So glad you guys into doing programming education. More I research, the more resources out there. We have to model taking risks!

    Moderator (Katherine): good luck!

    Moderator (LisaRittler): Gina: Wish me luck on class next week!

    Moderator (LisaRittler): Gina: Stand up for yourself and let your voice be heard

    Moderator (Sue): none here

    Moderator (Katherine): great advice! I feel like I've gained so much knowledge from this course and everyone's ideas so I'll be ready

    Moderator (Maria Droujkova): Great idea with the hand raising!

    Moderator (LisaRittler): Gina: yes- you can use P2Pu site to do task if you want

    Moderator (LisaRittler): Gina: use what we've already learned into task if you want...either post in our website or another one

    Moderator (Sue): I agree

    Moderator (Sue): I was

    Moderator (Meagan): edmodo is good

    Moderator (Meagan): Thanks

    Moderator (LisaRittler): Gina: ok- ..not as good...but the collaboration classroom is a good website & you have to accept students into classroom.. Get comfortable with the programming piece moreso than the website MOOC pice

    Moderator (LisaRittler): piece  

    Moderator (LisaRittler): Gina: Any other questions?

    Moderator (Sue): none here

    Moderator (LisaRittler): Nope

    Moderator (Katherine): nope!

    Moderator (Katherine): thanks everyone for another great chat! I always get so much out of these.

    Moderator (LisaRittler): Gina: Thank you everyone for all your input, life and classroom and how to incorporate. We get some great ideas on how to use and find resources. and again for preparing future generation. Look forward to hearing any controversies throughout week.

    Moderator (Sue): thank you!

    Moderator (Katherine): goodnnight all!

    Moderator (LisaRittler): Thanks Gina! Great Job...Nighty Night   

    Moderator (Sue): Good night, everyone

  • Maria Droujkova   April 20, 2013, 3:40 p.m.
    In Reply To:   Gina Mulranen   April 17, 2013, 8:36 p.m.
  • MgnLeas   April 13, 2013, 9:20 p.m. Here is the link for free tial of smartboard!

  • Maria Droujkova   April 9, 2013, 7:51 a.m.

    Monday, April 8 meeting link. We talked about issues of Interactive White Boards - tech support, teacher choice, guiding students and more!

  • Gina Mulranen   April 11, 2013, 8:50 p.m.
    In Reply To:   Maria Droujkova   April 9, 2013, 7:51 a.m.

    I'm so sorry I missed this session! I have always been interested in interactive whiteboards ever since I was introduced to it during my student teaching. My cooperating teacher taught with ALL Smart documents so I quickly had to learn how to prepare the Smart documents and save the written slides as documents for absent students as well. It was a HUGE learning experience for me.

    Sue also mentioned that her son's school uses the Promethean boards, which my school has 2 of. Unfortunately, because I was the last math teacher hired, I did not get one of the boards. With the budget, I probably won't be using one for awhile. However, I do want to be prepared to learn when I do get one! I also think more and more schools are getting this interactive whiteboard and I think it is very important to stay up to date with the technology that is out there!

    Lisa also mentioned about training with the whiteboards. I do agree that there is not enough training and technology support, especially at my school since it is so small and these boards are so new. Even though technology is wonderful, it frequently does not work for me either. One day my school lost its internet connection and I had to do an online activity on the dry erase boards. I have learned that you should ALWAYS have a backup plan for any piece of technology you use, from projectors to the internet to whiteboards.

    I really liked how everyone talked about problem solving with whiteboards and how many obstacles we have to encounter when we teach. I appreciate teachers SO much more because of their constant creativity. Not only are they creative with their lessons, but they also can problem solve right on the spot!

    Meagan, I LOVE the koosh ball idea! I do use Jeopardy and Connect Four as review games and that is a great idea to choose the questions. Even though I do not have a interactive whiteboard, I think I might use that with my projector agaisnt my whiteboard. Thank you!

    In response to the question about using the technology, I think that schools should ASK the teachers whether they would be committed to learning and using the whiteboards on a consistent basis BEFORE they purchase them. I think that some teachers are not interested in using them and do not feel like they need them so I do not think they have to have them or use them. They should be using the money to buy interactive whiteboards for teachers who are excited to put in the time and effort for the new technology!

    I am so glad that backwards learning has been brought up. My mentor mentioned this to me this year when I was worried about not getting through my Algebra 1 cirriculum fast enough to prepare for the Keystones. I think that this method of learning would benefit some students, but I do not think it would work for everyone, just like any instructional tool. I have had my students view a recorded lesson and then practice the concepts the next day and I have found that some students got it and some students were struggling. I think it is an effective tool, but I do not think we should be relying on it all the time. It is a great tool to switch it up!

    I found the video really interesting as well. I would have never though of using it for a music class. So cool! Again, I am so impressed with teacher creativity!

    I do not have any questions right now on the tasks for this week. It looks great, Lisa! Great job on runnning the discussion for this week. It was great!

  • Katherine Hanisco   April 27, 2013, 9:22 p.m.
    In Reply To:   Maria Droujkova   April 9, 2013, 7:51 a.m.

    I mentioned this a bit in my response to the tasks for this week, but I did fieldwork at Upper Dublin HIgh School which is a brand new building with high tech resources and interactive whiteboards in every classroom, and I saw almost no utilization of the whiteboards in all the math classes I observed. When I asked about it, I was told that there was no kind of training or support provided, so if teachers did not know how to use them, they were on their own to figure them out. It seems crazy that they would spend millions of dollars to build this beautiful high tech building and then not invest in the resources to take advantage of all of that. 

  • Maria Droujkova   April 4, 2013, 7:23 a.m.

    Wednesday,  April 3 meeting recording. Please add your comments if you missed it:

    There is a slider on the bottom that lets you scroll through the recording. If you slide it all the way to the right, you will see the full text of the chat. 

  • MgnLeas   April 6, 2013, 10:53 p.m.
    In Reply To:   Maria Droujkova   April 4, 2013, 7:23 a.m.

    I tried to listen to the meeting and got an error message. I am gonna try it again tomorrow and see what happens.

  • Maria Droujkova   April 9, 2013, 7:53 a.m.
    In Reply To:   MgnLeas   April 6, 2013, 10:53 p.m.

    I wonder if your browser cut off the link that was too long. Try clicking on THIS LINK that should not "wrap up" like that. The recording is there as of this morning: I checked.

  • MgnLeas   April 1, 2013, 4:40 p.m.

    I think eveyone should watch the show "Numbers". It is about a math professor and genius who helps the FBI solve crimes using math. He shows that numbers are everywhere and math can help in everything!

  • Maria Droujkova   March 31, 2013, 3:47 p.m.

    Wednesday, March 27 meeting recording:

    If you missed it, write a comment here.

  • MgnLeas   April 1, 2013, 4:36 p.m.
    In Reply To:   Maria Droujkova   March 31, 2013, 3:47 p.m.

    First, I am so sorry I missed last week. My son was up sick all night and I did not set an alarm because I am usually up at 10 in the morning! But we ended up sleeping until 11:30 (he did not slepp solid until about 7:30!)

    I agree with Gina when she was talking about education being the one thing that every country has the same goal. We all want our children to get the best education possible. Education is universal, everyone learns. As educators, we can look to other countries as a resource. We should be open to new and different ideas to enable us to be the best we can for our students ad our countries goals in education.

    I too was nervous about finding articles in Finnish and translating it. However, the Google translate worked great. I did have to go through a few articles to find what I was interested for. I did think after the fact, this would be a fun assignment for kids. If kids in you class speak other languages, have them search for things in other languages to help them see how ELL students feel all the time in our classroom. Have them walk in someone else’s shoes so to speak.

    I agree we can never have too many resources. Technology helps to create more avenues of resources. I have also learned through this class that there are so many free outlets out there to use. This helps to use the technology!

    I had fun learning about Finland and its education system. I actually just pasted the Praxis 2 and am getting my certification and looking for jobs. My husband suggested looking into other countries for the experience and I searched Finland!

  • SueSullivan   April 1, 2013, 11:37 p.m.
    In Reply To:   MgnLeas   April 1, 2013, 4:36 p.m.

    I hope your son feels better - it is SO scary when the children feel so horrible that they can't sleep!

    As parents (and teachers!), we need to sleep when we can so we can be mentally prepared (if there IS such a thing) for whatever life gives us - rest while you can!  One of my favorite things about tech is online classes and the flexibility they offer  :) 

  • MgnLeas   April 2, 2013, 12:20 p.m.
    In Reply To:   SueSullivan   April 1, 2013, 11:37 p.m.

    Thanks. He had an ear infection (we took him to the dr) then about two days after we started his meds he got a terrible cough. I think the combination just made him miserable. We slept in our rocking chair (one of the amzing cushiony ones I got while pregnant), so he could be more upight to help him. He is doing much better now!

  • This comment was deleted.
  • Lisa Ritt   March 26, 2013, 11:39 a.m.
    In Reply To:   Maria Droujkova   March 26, 2013, 11:37 a.m.
    I figured it out!! sorry to bother you!!! -LIsa "Be the Change You Want to See in the World" My contact info: email: cel ph# (215) 740-6036 Our OceanCity, NJ condos are available all year!
  • Katherine Hanisco   March 11, 2013, 5:22 p.m.

    I think my biggest concern is designing tasks that are educationally valuable to everyone. In a course at this level, I think that “busywork” is just about the worst kind of assignment. Everyone is here to gain practical knowledge that will help them be a better teacher, and so I’m worried about how to design tasks that aren’t a waste of anyone’s time.

    I also have concerns for how to balance specificity with freedom to be creative and make tasks personally relevant. One of the things I have found most valuable about this course thus far is that the tasks have been designed in such a way that I’m able to bring a lot of myself into them, which makes it so much more meaningful to me. But I also appreciate clear guidance and direction, especially when the topic is unfamiliar to me. I hope that I am able to design tasks that are both meaningful and understandable. 

  • Lisa Ritt   March 10, 2013, 8:11 a.m.

    HI everyone. My first concern about my task week is keeping it both interesting and appropriately challenging for everyone. Since I'm not teaching now but hoping to soon I am concerned that my subject of SMART BOARDS- why they work or don't work may be too....elementary for my classmates here?

    But- mostly what I'm hoping for is to help all of us  find lots of cool ways to use smart boards (& the like)-- to find ways that all of these smart boards can be utilized to best serve our students. Also, to look for troubleshooting training as its seems to be something I hear so many teachers complain about. 

    I also feel like Gina in that I am NOT at ALL a smart board expert...quite the opposite so I WILL be doing the same work that my classmates are doing as I present my task & I'm hoping that will be ok. Prior to my task, I should have a little more experience on smart board technology so hopefully that will help!


  • Maria Droujkova   March 9, 2013, 8:53 a.m.

    Wednesday, March 6 recording of the live meeting:

    We kept it short, because of where we are in the semester. If you missed the meeting, please answer the following:


    What are some of your concerns about your role as a leader of a week in this course?

  • Gina Mulranen   March 9, 2013, 9:33 a.m.
    In Reply To:   Maria Droujkova   March 9, 2013, 8:53 a.m.

    In response to the recording and the reference to my experience as a cyber teacher, I would be very willingly and excited to help out with blended learning since I have a lot of experience teaching for 3 years in a cyber school. I post cyber assignment weekly and have used a variety of different strategies to structure those cyber days where the students are learning and working at home.

    One of my concerns about my role as a leader of a week on programming is my own personal skill level with programming. I have only worked with Scratch and the java language but have heard of Python as another programming software used with high school students. I am worried I won't be able to answer some questions if I'm not already an expert in that field.  I am really using this tech week as an opportunity to explore, share what I find, and exhance my understanding through the feedback and experience of my fellow classmates and professor.

  • Maria Droujkova   March 9, 2013, 10:03 a.m.
    In Reply To:   Gina Mulranen   March 9, 2013, 9:33 a.m.

    Gina, thank you for posting your concern! It happened so that I wrote something this very morning that I think is related. Serendipity: I already have the document opened in another window, so I am pasting it here. Since I am still working on the essay, I would love to hear from you and anyone else who happens to read it - does it make sense? It's about kids, but I think it applies. It's a response to James Tanton's ten techniques of problem solving, which you can find here:


    Another frequent question: “How can I help my child if I can’t solve some of these problems myself?” Your child gives you a second chance in life - a chance to heal your relationship with math. Let your kid be your role model! Borrow plenty of childish playfulness and curiosity. In particular: 
    • Do successful flailing (technique #1) and other nine problem-solving techniques together with the child! Even if you don’t solve the problem, you will spend quality time with math, and learn the techniques.
    • Give yourself the gift of time. Do you think you and your child would solve the problem if you had three hours to explore it? If so, give yourself permission to spend the three hours, even if you have to spend them over the course of the next month. Math is supposed to be slow.
    • Talk to others. Talk to the child, or ask your friends and their kids about this neat frustrating puzzle, or post it to social networks like Twitter or Facebook, or use our Question and Answer tool, or comment on this post. Talk about your math - this is the eleventh problem-solving technique!
  • Gina Mulranen   March 9, 2013, 10:23 a.m.
    In Reply To:   Maria Droujkova   March 9, 2013, 10:03 a.m.

    I am a firm believer that talking about a topic will make you more fluent and knowledgeable about the issue. This is why I always tell my students that a great study technique is to teach someone else how to do a problem that you were using to practice for the test. By teaching it to someone else, you are achieving a higher level of understanding.

    I also like your point about failing to solve a problem. Think about how many inventions involved successive and frequent failures. Learning how NOT to do a problem is even more valuable than doing the problem right and moving on. You learn the negative and positive exemplars of the topics and achieve a more well-rounded understanding of the topic.

    I definitely think the essay that you are writing makes sense and can be applied to a variety of age groups, even parents! I know some many of my parents reach out to me and ask me what they can do to help their kids. I would love to see the finalized essay when you are finished! Thank you for sharing!

  • Maria Droujkova   March 5, 2013, 5:56 a.m.

    Here is a much-loved 1970s article "Mathematics as a creative art?"

    And here is a sad story from 2002, about the same topic, called "A mathematician's lament"

    Times change?

  • Maria Droujkova   March 4, 2013, 6:32 a.m.

    Several people here talked about virtual graph paper. Here is an implementation I like:

    Check out the comments on the blog post, too. They talk about people's enthusiasm for a good manipulative. 

    • Awesome! Virtual Graph Paper + iPad + Dungeons & Dragons = Lots of awesomesauce
    • Your virtual graph paper is a perfect match for a classroom exploration I have planned. THANKS!
    • This is amazing! Wish I could write code cause I have a few great ideas to add to this! Thanks a million!
  • Gina Mulranen   March 4, 2013, 12:09 p.m.
    In Reply To:   Maria Droujkova   March 4, 2013, 6:32 a.m.

    Wow! This is a fantastic tool!!! Thank you for sharing!

  • Maria Droujkova   March 2, 2013, 6:39 a.m.

    Here is the recording of the February 27 meeting

    Question 1

    Among other things, we discussed the order of student-led weeks in the second half of the course. The four people present wanted the first four weeks, namely, weeks starting at

    March 17

    March 24

    March 31

    April 7

    Gina and Green Machine, if it is okay with you to lead the following two weeks, please let me know which of the two:

    April 14

    April 21

    If not, we will work on swapping dates around!

    Question 2

    Make a particular example of how a piece of mathematics education technology can help you and other teachers make large changes in your students' lives, even in the face of resistance from powerful education-related systems. This had been discussed in the last ten or so minutes of the meeting.

    Transcript of the chat (I took notes when people spoke):


    Joined on February 27, 2013 at 10:02 AM
    Moderator (Maria Droujkova): Meagan: No unified definition of ethnomath!
    Moderator (Maria Droujkova): Katherine: Some of these issues get lost among more directly curriculum-related issues.
    Moderator (Maria Droujkova): Lisa: I saw a disabled boy on TV, who has a robot going to classroom for him. He can do everything through the robot.
    Moderator (Meagan): Do you remember what news site?
    Moderator (LisaRittler): I"ll have to look it up! sorry I dont
    Moderator (Meagan): NO worries Thanks
    Moderator (LisaRittler): it was real!      
    Moderator (Maria Droujkova): yay
    Moderator (Meagan): Yeah welcome
    Moderator (LisaRittler): here is link:
    Moderator (LisaRittler):
    Moderator (Meagan): thanks lisa
    Moderator (Maria Droujkova): Do any of you want to go first?
    Moderator (LisaRittler): thank you Meagan!!!!!
    Moderator (Sue Sullivan): I'll go next
    Moderator (LisaRittler): I'd love the first week of April?
    Moderator (LisaRittler): 2nd week is great too
    Moderator (Meagan): We talked a llittle before about teaching teachers type of tasks
    Moderator (Maria Droujkova): What populations do you care about for math accessibility?
    Moderator (Maria Droujkova): Katherine: I care about girls in math, accessibility to STEM. I've been hearing a lot of the stories about the message girls are getting from the young age, that they are good at writing and reading, and boys are good at math. There are simple and reasonably implementable things parents and educators could do, such as using different language.
    Moderator (Maria Droujkova): Atiba, welcome
    Moderator (Maria Droujkova): You can type in here if the microphone isn't working
    Moderator (Maria Droujkova): Meagan: another population I care about is deaf population. If I can sign better, I can reach more people.
    Moderator (Maria Droujkova): Sue: Like you, Meagan, I am also drawn to middle school. I am interested in students in low socioeconomic status schools. There is a big gap between haves and have-nots. It's a big social issue
    Moderator (Green Machine 2): I can't really say I have determined population. I strive towards being flexible and an excellent educator; where I am able to teach across all grades. I can say that I seem to be most comfortable with middle or high school scholars. I am used to dealing with an "urban" population or low income population.
    Moderator (Maria Droujkova): Lisa: Among these kids, there are also a lot of people with emotional and behavioral issues. Some kids may be learning slower than others. In many cases, behavioral issues are periodic, but the student are put in a category of "un-able" or "non-capable" of doing math.
    Moderator (LisaRittler): Amen!
    Moderator (Green Machine 2): lol
    Moderator (Maria Droujkova): What do you hope to achieve for the society at large, through your math intervention for your population?
    Moderator (Green Machine 2): For me, it would be economics and the power of unity.
    Moderator (Maria Droujkova): Meagan: I hope to show that math is not hard if you stick with it, and that they can do it and be a math person
    Moderator (Green Machine 2): I also aim to influence their nutritional habits with the aims that it would help aleviate some behaviors that we deal with in the classroom.
    Moderator (Maria Droujkova): Katherine: I hope to make it so women are more equally represented. I know in physics especially, women have low percentage. In engineering there may be hostile working environment, where women are expected to take notes or are viewed as junior. I want to change that attitude.
    Moderator (Maria Droujkova): Katherine: We are suffering if we are only using half a population for our sciences, for the society in general.
    Moderator (LisaRittler): INspire the Desire!
    Moderator (Maria Droujkova):
    Moderator (Green Machine 2): I would say economics and the power of unity because I am used to same picture in many "urban" neighborhoods. Corner stores, chinese stores, delis, liquor stores, nail salons, barber shops, and etc... Nothing is the matter with this picture excpet for the fact that majority of these businesses are not owned by the major culture in the area. I also feel as though many of these businesses do not carry the interest of the community. I always strive to have the scholars create entrepreneurship oppotunities.
    Moderator (Katherine): I didn't know I had that selected, sorry
    Moderator (Maria Droujkova): Sue: I want to expose people to different types of math, so they know what is out there and there is more interdisciplinary approach to the society.
    Moderator (Sue Sullivan): Green Machine - love your approach, it relates math to society
    Moderator (Maria Droujkova): Lisa: Math allows you to do things in life - so many that without it, you could be lost. You just feel sorry that people don't feel capable of it, from the early age. That's what I want to change.
    Moderator (LisaRittler): Be the Change you want to see in the World! That guy was smart who said this !!
    Moderator (Maria Droujkova): Do you think teachers can change the world?
    Moderator (Meagan): Yes of course
    Moderator (Meagan): Great comment Lisa
    Moderator (Green Machine 2): Not within the construct of the present educational system we have developed.
    Moderator (Sue Sullivan): Love that quote!
    Moderator (Green Machine 2): Ghandi said that quote.
    Moderator (Green Machine 2): It is possible but I believe that many educators don't realize the seriousness of change,
    Moderator (Meagan): Acts of random kindness
    Moderator (Sue Sullivan): Green Machine, I agree, I think many become burned out and disillusioned
    Moderator (Green Machine 2): true.
    Moderator (Green Machine 2): I have seen many burn out
    Moderator (Green Machine 2): but isn't that design of our educational system
    Moderator (Sue Sullivan): the system certainly doesn't help
    Moderator (Green Machine 2): For instance, we know that standardized tests like the PSSA and Keystone, drive how many of the schools operate
    Moderator (Sue Sullivan): yup   
    Moderator (LisaRittler): there are always obstacles! But even if you reach 1 kid...make a difference in 1 life, SUCCESS
    Moderator (Green Machine 2): true
    Moderator (Maria Droujkova): How can tech help us in our big goals?
    Moderator (Maria Droujkova): one microphone at a time, please - echo
    Moderator (Maria Droujkova): Question: How can tech help us reach goals and become powerful, even if there are big systems that work against our goals.
    Moderator (Maria Droujkova): Lisa: There are a lot of ways outside of classroom that technology allows us to have, to find information we don't know existed. It's a great and available tool.
    Moderator (Maria Droujkova): Katherine: Us as educators contributing to the global community of education online, with free and open exchange of ideas, even by leaving comments, uploading projects - all that builds the community. Now you have resources, a huge network of people who are on your side. It's not just you in the corner.
    Moderator (LisaRittler): helps students feel that they have friends in a bigger community...if they suffer within the classroom with feeling uncomfortable with their peers
    Moderator (Sue Sullivan): hello?
    Moderator (Maria Droujkova): Katherine: Students who don't have local options can take classes online and have opportunities.
    Moderator (Maria Droujkova): Sue, you have a bit of lag
    Moderator (Maria Droujkova): can you talk?
    Moderator (LisaRittler): Its hard to find educators in HS in inner city to teach calculus , physics, etc
    Moderator (Maria Droujkova): Meagan: Technology can help us reach a larger pool of people. It can help us make those small steps into a little bit bigger steps.
    Moderator (Maria Droujkova): Sue: Technology can be a way to circumvent the system, where you can find alternative ways of doing things
    Moderator (Katherine): Lisa, the principal of the school was trying to implement a program where advanced students completed their high school requirements in 3 years and in the 4th year, they were still in high school but would take classes at the community college so they had access to more advanced courses, but there were issues with how to get the students there, textbooks, etc
    Moderator (Maria Droujkova): Can you provide a particular example of a particular tech subversing and distrupting the status quo in education?
    Moderator (Maria Droujkova): Sue: The internet makes information available, so it changes the privacy and the spread of information.
    Moderator (Sue Sullivan): oops sorry didn't hear the 'education' part
    Moderator (Maria Droujkova): Have another go, Sue!
    Moderator (Maria Droujkova): we can hear
    Moderator (Sue Sullivan): i can hear
    Moderator (Maria Droujkova): Meagan: solvers that just give answers can change things
    Moderator (Maria Droujkova): Sue: Students don't have ways to evaluate information
    Moderator (Sue Sullivan): we can reach more populations
    Moderator (Sue Sullivan): such as voice-recognizing software
    Moderator (Sue Sullivan): to help those who cannot use their hands
    Moderator (Green Machine 2): Solar technology would be a great social agent of change.
    Moderator (Green Machine 2): I have seen trash compactors that a run on solar energy downtown and other parts of Philadelphia.
    Moderator (Maria Droujkova): Meagan: In software like Geometer's Sketchpad, you can manipulate things in ways you could not before, which is hard on paper
    Moderator (Sue Sullivan): Megan, I love that too!
    Moderator (Green Machine 2): Maybe even robots that run off solar energy that constantly keep the streets clean.
    Moderator (LisaRittler): the 3d element online is amazing for math learning
    Moderator (LisaRittler): thats incredible Katherine!!! so cool!
    Moderator (Maria Droujkova): Katherine: Schools can get involved in global math projects, not just with local people. Students in that isolated school in Australia learned from experts in America.
    Moderator (Green Machine 2): Educators could also use video conferencing to observe other educators across the globe and share best practices so that all of our children are successful
    Moderator (Green Machine 2): I believe we have a lot that we can gain from observing the structure of schools outside of the USA
    Moderator (Maria Droujkova): Global exchange of ideas is very powerful, Atiba
    Moderator (Katherine): Atiba, I agree!
    Moderator (Maria Droujkova): Lisa: Not being in front of classmates can make people feel better and more confident. But how can we keep kids safe online?
    Moderator (LisaRittler): Thanks everyone! Always great to hear these wonderful ideas and thoughts!
    Moderator (Meagan): No questions here
    Moderator (Sue Sullivan): No questions
    Moderator (Sue Sullivan): Have a good week, everyone!
    Moderator (Meagan): See ya next week
    Left on February 27, 2013 at 11:05 AM
  • Gina Mulranen   March 2, 2013, 8 p.m.
    In Reply To:   Maria Droujkova   March 2, 2013, 6:39 a.m.

    Question 1

    I would prefer to do the week of April 14th with computer programming. I think Green Machine's topic of robotics would be a great one to follow mine if they chose to do that topic.

    Question 2

    In response to Lisa's comment about the commerical with the robot going to classes for a student at home, I was also thinking about this class when seeing that commerical. It still amazes me how far technology has come and how much it can impact our lives. For that student in the commerical, he has on a medical bracelet, which makes the audience assume that the student is on medical treatment and can not attend school. This robot travels to each one of the child's classes and the student's head is broadcasting from the robot's head! Everything looks like it is in real time, which allows the student to interact with his classmates and his teacher just like as he would in class. That is just...incredible. Being about to give a student back a little taste of normalcy is priceless.

    I also agree with the comments made in the recording about being able to access and share information with a large audience of people around the world with the same interests. For example, I have been using this app on my iPad called Educreations. This is a whiteboard tool that allows teachers to record lessons and share them. I have used this tool for a whiteboard while I was tutoring and also to record lessons that I can post for students that are absent. I emailed the creator of the app about uploading PowerPoints and he said he is working on that to enhance the recorded presentations. I love to see all the different lessons from teachers all of the world on a variety of topics. It is like we unite as teachers around the world through these educational online tools. is also a great site where teachers can create games and share them so other teachers can use them if they are assessing students on the same topics. I use a lot of these shared websites and are very grateful for them. We need to work smarter as teachers and use the resources we have in this techonology era. No need to reinvent the wheel anymore, so to speak.

  • Maria Droujkova   March 6, 2013, 2:36 p.m.
    In Reply To:   Gina Mulranen   March 2, 2013, 8 p.m.

    I am so happy to hear you are reaching out to people who make apps with feedback and request of features. I wish more teachers would do that! When we leave feedback and interact with authors, the community benefits. Most authors love this, as well.

  • Lisa Ritt   Feb. 24, 2013, 12:38 p.m.

    HI guys,

    I am a huge music lover! I find that most kids immediately enjoy themselves & focus their attention on a song they like if all of a sudden, when they are distracted by something else or bored or just not paying attention, if all of a sudden, you sing or play music or really anything with a beat, you get a focused postive resonse from kids of all ages. I use this alot when I'm directing a musical or if I walk into a room of kids and I need their attention.

    Here is a really cool link where kids have to find beats per minute in a song. I think this would absolutely be something I'd use in a middle school math class:

  • Green Machine   Feb. 25, 2013, 2:11 a.m.
    In Reply To:   Lisa Ritt   Feb. 24, 2013, 12:38 p.m.

    I too, am a huge lover of music. I am constantly aiming to develop new ways that mathematical concepts can be taught through lyrics, rhyme, or music. I found a few videos on youtube that captured what I am to do. I really enjoyed the videos I found because they were created for high school concepts, along with music or instrumentals that the scholars could relate. I believe that fact that they were songs that the scholars could recognize made a huge difference. Some people may not agree with the music that majority of the youth listen to, but it is equally as important for us as educators to know what they like so we can make our lessons relevant and engaging. I like to stay on top of what they listen to because it gives me a frame of reference to work when I develop new songs that incorporate or teach math concepts.

  • Katherine Hanisco   Feb. 21, 2013, 8:13 p.m.

    Hi all,

    Since I've been talking so much about NASA using social media to connect with the public (and young people in particular) I just wanted to share this info: tomorrow, 2/22, at 10:30 am EST, NASA is hosting a Google+ hangout with astronauts on the International Space Station. You can submit video questions and they will select a few to answer live during the chat. They say that unique and original questions are more likely to be selected, and I think that could be a fun assignment for a class - incorporate material from lessons to craft a thoughtful, informed, interesting question for the astronauts.

    I just wanted to share the link in case anyone is interested in checking it out!

  • SueSullivan   Feb. 21, 2013, 9:10 p.m.
    In Reply To:   Katherine Hanisco   Feb. 21, 2013, 8:13 p.m.



    Thanks for the link - it's another great way to show the 'human face' of mathematics; the contributions that the astronauts are making to math, science, and the humanities is a discussion unto itself.  I've seen the ISS fly over many times, and often wonder what the astronauts are thinking about as I watch from my yard or campsite.

    I'm sure you already know about this, but if anyone else is interested, gives excellent information about viewing the International Space Station as it flies overhead; there should be excellent viewing opportunities on the 22nd and 23rd of February, weather permitting.

  • Maria Droujkova   Feb. 21, 2013, 12:24 p.m.

    This is the recording of Week 6 meeting, on February 20:

    There are some issues with Java right now. You may need to download the latest version of Java, and then to tell your computer to open that file with Java.

    If you missed the meeting, here are two questions to ponder...

    Bonus reading -- Ethnomathematics and symbolic thought: The culture of Dogon

    Dogon Math House

    Question 1

    What are main characteristics of (1) sciences (2) mathematics and (3) humanities - from the point of view of a math ed person, that is, yourself in your professional role?

    Question 2

    Find some similarities and differences between (1) sciences and math (2)sciences and humanities and (3) math and humanities. What are some dimensions or aspects you find interesting for these comparisons?


    And here is the full transcript:


    Joined on February 20, 2013 at 10:07 AM
    Moderator (Meagan): yeah i am here
    Moderator (Green Machine): yay. lol.
    Moderator (Maria Droujkova): we can
    Moderator (Green Machine): you got it
    Moderator (Maria Droujkova): Meagan: I am frustrated W|A does not show enough of step-by-step. But there are tools that do, I am going to find that one site that did it well.
    Moderator (Maria Droujkova): yay!
    Moderator (Meagan): Happy Birthday!!!!!
    Moderator (Maria Droujkova): Katherine: It's easy to be a critic when you are watching it, but should I be talking about it as a back-seat driver? I like reading everybody's thoughts, though, so critique is helpful.
    Moderator (Maria Droujkova): Happy fifth!
    Moderator (Maria Droujkova): Sue: I enjoyed evaluating sites and developing criteria for it. I can now effectively evaluate sites.
    Moderator (Maria Droujkova): we can hear
    Moderator (Meagan): Happy Birthday
    Moderator (Sue Sullivan): happy birthday!
    Moderator (Maria Droujkova): Atiba: Celebrated my 31st birthday. Looking forward to seeing that topic of computer-based math. Some of the programs have good aesthetics, and it makes me a fan.
    Moderator (Maria Droujkova): Happy birthday!
    Moderator (Maria Droujkova): What are some deep differences between sciences, mathematics and the humanities?
    Moderator (Maria Droujkova): Meagan: When I think of humanities - cooking, sewing, workshop, metalworking, hands-on and practical. And science is application of math.
    Moderator (Maria Droujkova): Katherine: When I think about math and science, especially the scientific method, there is a process of observing nature. The experiments and observations may or may not support your hypothesis, but feelings don't matter. In the humanities, what everybody's think or feels, the human condition, is the critical part of the humanities. You are looking at the human piece of it. But in science and math human feelings are irrelevant.
    Moderator (Maria Droujkova): Atiba: Math is pretty much the numbers, it can be applied, and the educator can make it happen in the classroom through experiments. A lot of science is theory + application, where you can apply math in observation, the scientific process, the theory, the hypothesis, the outcome. The humanities can be a combination of theory and application, or human experience and opinions. In math and science, a lot of things can be proven, but in humanities, things change based on different variables.
    Moderator (Maria Droujkova): Sue: Math and science tries to explain things, but parts of humanities focus on CREATING, and often for aesthetic purposes. But math is not focusing on that.
    Moderator (Maria Droujkova): Meagan: I did not even think of art and music, but they are mathematical. Music, in the way it's written. There may be something mathematical within the art itself.
    Moderator (Meagan): awesome idea
    Moderator (Maria Droujkova): Sue: I will do a lesson about fractions using music.
    Moderator (Maria Droujkova): Katherine: There are differences between the three, but a lot of the time, there is a big line separating them. But they are all related, they overlap. They are kept too separate.
    Moderator (Maria Droujkova): Sue: I was told I will never have an appreciation of culture, because I like math and I am weird
    Moderator (Maria Droujkova): (everybody relates)
    Moderator (Sue Sullivan): oh no!
    Moderator (Meagan): Dr. Freidler?
    Moderator (Maria Droujkova): (many anecdotes)
    Moderator (Katherine): "hate it less" - a high compliment from an 8th grader!
    Moderator (Maria Droujkova): Indeed
    Moderator (Sue Sullivan): very true
    Moderator (Maria Droujkova): What are some differences between math and science? Similarities?
    Moderator (Sue Sullivan): well put
    Moderator (Maria Droujkova): Katherine: Math can be applied, but does not have to be. Even numbers: 5+3=8 whether or not you have 8 things to count. Math is the language of the universe, especially physics. In science you can have some observations, like speed of light - and it does not depend on whether you derive it. In math, observation is secondary, you can find things theoretically.
    Moderator (Maria Droujkova): Atiba: One major difference is topics being taught. Math is abstract, but in science, you can talk about things like human body or biology. But subjects like chemistry and physics are math-intensive.
    Moderator (Maria Droujkova): Meagan: The difference is in how you prove things, too.
    Moderator (Maria Droujkova): What about creation?
    Moderator (Maria Droujkova): Sue: You can observe math being applied all around us. Speaking of comment, many poems by Shakespeare are in a particular form - a math expression, in a way.
    Moderator (Meagan): The Golden Ratio
    Moderator (Maria Droujkova): aye! great example
    Moderator (Maria Droujkova): Katherine: "The unreasonable effectiveness of math in sciences" - math describes nature in incredibly accurate ways. Years later it turns some abstract branch of math applies to something. So people are creating math and then - wow! Turns out complex analysis is needed, for example. You create even in the math itself, without going to the humanities.
    Moderator (Maria Droujkova): Atiba: Math originally was created through observation, back in the day when they built pyramids or mapped stars, or the group of nations in Africa that put together maps of the universe. But then people began to use creativity to develop new aspects of math and new fields of math. I am also thinking about spiritual realms where math can develop.
    Moderator (Green Machine): Dogon
    Moderator (Maria Droujkova): What are some similarities and differences between sciences and humanities?
    Moderator (Maria Droujkova): (Oh, and you can type additional thoughts here any time)
    Moderator (Maria Droujkova): (chat and listen)
    Moderator (Maria Droujkova): Katherine: connections can happen in aspects such as cultural anthropology
    Moderator (Maria Droujkova): Sue, can you type your point, since I missed typing it (behind)
    Moderator (Maria Droujkova): Atiba: Think about cooking - it has certain chemisty to it, reactions in it, what happens when you freeze it or heat it.
    Moderator (Sue Sullivan): Great point - also ties in with how availability of food influences development of human culture
    Moderator (Sue Sullivan): Meagan, love this idea - students often have no idea of the relationship between science and food
    Moderator (Maria Droujkova): Meagan: I have a book of bath-time experiments for toddlers, this connects beauty, nature, humanities (bubbles are beautiful).
    Moderator (Green Machine): another nation are the Mayans as well
    Moderator (Maria Droujkova): Mayans had amazing math
    Moderator (Maria Droujkova): Katherine: Sometimes models and their authors become too accepted by the scientific community. So there are psychology and sociology reasons in science. You can't be objective all the way - there are still humans doing it.
    Moderator (Maria Droujkova): Reference: Kuhn on scientific revolutions
    Moderator (Maria Droujkova): Sue: A lot of cultural phenoma are shaped by conflicts between religions and science, like creationism
    Moderator (Sue Sullivan): Fascinating!
    Moderator (Maria Droujkova): Math and humanities now?
    Moderator (Maria Droujkova): Meagan: We did a whole unit on the Golden Ratio. There is a project to find the Golden Ratio in your face. I had to be careful to avoid them picking on one another. It's fascinating, because many drawings have this ratio, and it pops up in nature.
    Moderator (Maria Droujkova): A lot of things humans find appealing have mathematical foundations.
    Moderator (Maria Droujkova): lag
    Moderator (Maria Droujkova): Katherine: One place where math and the humanities overlap is philosophy, especially logic. A lot of logic questions felt like mathematical proofs to me. Inductive vs. deductive reasoning applies to both, for example.
    Moderator (Maria Droujkova): Dimensions... Who creates it? The human opinions/thoughts/ideas and rationality/objectivity. Cultures, cultural differences.
    Moderator (Sue Sullivan): I enjoyed hearing everyone's ideas - it was a great learning experience.
    Moderator (Maria Droujkova): Katherine: Are we math persons or non-math persons? Do we have to divide?
    Moderator (Meagan): We can get to all students through math through whatever they love
    Moderator (Katherine): I agree!
    Moderator (Maria Droujkova): Atiba: People here "math" and think of astronauts, engineers and other advanced people. I developed curriculum for daycare, and I realized a lot of people have phobias about math. But it's everywhere - cooking, money (everybody relates to it!), all simple connections. People would love math if they connected through what they love. Building empires, looking at celebrities - something that interests people.
    Moderator (Maria Droujkova): Sue: A lot of people don't even know what they dislike about math, why they don't like it. Negative publicity and fear of unknown can develop into a phobia.
    Moderator (Maria Droujkova): Thank you all
    Moderator (Meagan): Thanks have a great week
    Moderator (Katherine): my daughter wanted to say hello to everyone
    Moderator (Sue Sullivan): Katherine, enjoy your day - children's birthdays are special for parents as well   
    Moderator (Katherine): thanks!
  • Gina Mulranen   Feb. 23, 2013, 3:47 p.m.
    In Reply To:   Maria Droujkova   Feb. 21, 2013, 12:24 p.m.

    Question 1

    Here is a great comic that I have in my classroom that I thought everyone might enjoy:


    I think the characteristics of math that applies to so many different disciplines are the different problem solving techniques and focus on logic and critical thinking. This can really apply to any field of study. When I think about the humanities, I think of art and music and history. Guess what? Music is based on math - fractions of a beat, rhythm, etc. And art? Yep. That is math based too! Proportions are used to gain forced perspective and scales are used to create scale drawings. Of course there are many different characteristics that makes each study unqiue, but I really believe that the skills you learn in math class can really extend past the classroom.

    I also wanted to join in the conversation that everyone was having on these "weird" math majors. All of my close girl friends from high school were history, PR, graphic design, or social work majors so, of course, they did not understand my excitement when I taught FOIL for the first time or sang the quadratic formula. Yep, they think I'm pretty weird too. Thankfully, I have a boyfriend in the Air Force who deals with math everyday when loading planes and he enjoys math puzzles with me. I do have a very strong passion for the subject of math and my students always comment on my enthusiasm when I teach. It is so important for me to get kids excited about math again because I felt like such an outsider throughout my schooling as the kid who liked math. I think that if students enjoyed and appreciated the subject more, they would get more out of it like the problem solving techniques and the ability to think outside the box.

    Question 2

    I really like how the Venn Diagram that was used in the recording as a visual to help relate these different fields of study. I am a very visual learner, so that was very helpful.

    The big connection I see between science and math is the step-by-step processes, the calculations, and the problem solving. Science involves a lot of hypotheses, experiments, and observations, which can involve a lot of hands-on activities. Math can involve observations in patterns and formulas, that can lead to really interesting student-discovery learning. Both math and science involves a lot of step-by-step processes and calculations, which is why people connect these two subjects easily. I think the harder subjects to connect are math and science to humanities. That is what I try to do with the projects I assign to my students.

    I think that science explains a lot of different humanities concepts. In terms of music, sound waves and the different frequencies produced by different notes is a great way to connect science and humanities. I also think that the scientific process can be applied to a lot of humanistic ideas like cooking, which Abita referred to. It is not just about the chemical reactions to create the different types of food, but also the process of testing and adding new spices to improve a reciepe.

    Between math and humanities, I think I agree with Katherine's comments in the recording that math can explain a lot of natural phenomenons. I also agree with Abita's comment about math developing over the course of history through observations, as well. I also think that math is related a lot to art. I just had my Pre-Algebra students create scale drawings using proportions. Even my students who admitted that they were not artsy created these amazing enlargements. Proportions can also be used to create forced perspective in drawings as well. This technique actually dates back to the Renaissance! I also really enjoyed Meagan's comments about the Golden Ratio. What a neat project to give to students to explore the ratios in the human face! So neat! I think activities are great to remind students the connections that math makes with all these different subject areas.

  • Lisa Ritt   Feb. 24, 2013, 6:05 p.m.
    In Reply To:   Maria Droujkova   Feb. 21, 2013, 12:24 p.m.

    Hi Maria,

    for some reason, I started with the bonus reading. To tell you the truth, I feel lost with it. I have to do more research on Dogon before I can have any reall understanding of just what is being explained in the article. A good bit over my head at this point! 

  • Lisa Ritt   Feb. 24, 2013, 7:04 p.m.
    In Reply To:   Maria Droujkova   Feb. 21, 2013, 12:24 p.m.


    Sorry I missed this week! Looking forward to next week! Thanks for all your great comments!

    Week 6: Pondering question 1:

    As a math ed teacher, I see math mostly as the study of relationships of numbers. I don’t think I would be a good math teacher without humanizing these numbers. In my education, I didn’t experience my Math teachers doing this as often as they could have. The relationship of math to science & the humanities is how they both have a basis in math. In studying science or humanities, you have a clear math basis. You may not be out to prove something to the kind of ump-teenth degree like we do in math…but you need math concepts to create decent hypothesis, don’t you? I started my thinking with looking up definitions:

    According to BING, science : study of physical world: the study of the physical and natural world and phenomena, especially by using systematic observation and experiment…branch of science: a particular area of study or knowledge of the physical world…systematic body of knowledge: a systematically organized body of knowledge about a particular subject

    According to Wikipedia, humanities :are academic disciplines that study the human condition, using methods that are primarily analytical,[citation needed] critical, or speculative, as distinguished from the mainly empirical approaches of the natural sciences.[citation needed]

    According to BING, math·e·mat·ics: study of relationships using numbers: the study of the relationships among numbers, shapes, and quantities. It uses signs, symbols, and proofs and includes arithmetic, algebra, calculus, geometry, and trigonometry.calculations: the calculations involved in a process, estimate, or plan

    Question 2: On this website , I found some nice correlations between math & science:

    *Algebra deals with general statements of relations, utilizing letters and other symbols to represent different values.  Used in science to develop formulas to find an unknown. 

    *Geometry deals with deduction of properties, measurements, and relationships of points, lines, angles, and figures in space.  It includes many different disciplines that try to describe the world.  Used in science to observe and describe.

    *Euclidean geometry deals with a flat world that states that parallel lines are always parallel and never intersect.  Euclidean geometry is our way of measuring on Earth.  Used in science to observe and describe things on Earth.

    *Riemannian Geometry deals with a spherical world that says parallel lines will intersect.  This takes into consideration,  the Universe may be a closed surface.  Used in science to observe and describe throughout the Universe.

    *Trigonometry deals with the relationship between angles and sides.  Used in science to help determine where the location of certain events are, like earthquakes, planets, stars, and many other things that we cannot directly measure.

    *Calculus refers to a large branch in mathematics that can solve many ways to measure (like volume or area) using complicated surfaces.  It is used in most branches of science to derive answers that cannot be measured directly.


    2)        This was a cool article about this subject. I didn’t agree with everything said in this article, but I found it a very interesting read.

    Here is a picture from it:



    Another cool read…on his website, James Joyner says “..Rather than requiring all students take math and science classes aimed at future engineers and physicists, wouldn’t we be better served having them focus on an increased understanding of how math and science effect the world around them?

    I absolutely agree with this statement. When you’re in middle school & high school, the feeling of “Why should I be concerned about this? …why should this be important to me is constant in many students’ minds. How math, science & the humanities are interlaced in such meaningful ways can be so interesting to explore with students. This would be where humanities comes into play. Science being filled with experiments which require data collection in mathematical formats. The experiments studying human reactions in physical scenarios….which of course brings in humanity.



  • SueSullivan   Feb. 26, 2013, 4:39 p.m.
    In Reply To:   Lisa Ritt   Feb. 24, 2013, 7:04 p.m.

    Hi Lisa,

    Love your comments for Question 2 - these would be great to post in the classroom, as they not only give definitions, but might spark students' interest in a particular concept (such as a "flat world" or "spherical world").   Thanks for posting!

  • Maria Droujkova   March 2, 2013, 6:51 a.m.
    In Reply To:   Gina Mulranen   Feb. 23, 2013, 3:47 p.m.

    Gina, a lot of what you are talking about relates for me to the term "mathematical thinking." For example, check out the syllabus of a MOOC (massively open online course) Keith Devlin is about to start at Coursera:


     1.  Introductory material
     2.  Analysis of language – the logical combinators
     3.  Analysis of language – implication
     4.  Analysis of language – equivalence
     5.  Analysis of language – quantifiers
     6.  Working with quantifiers
     7.  Proofs
     8.  Proofs involving quantifiers
     9.  Elements of number theory
    10.  Beginning real analysis
    Problem-solving and abstract modeling can be done in any field, from cooking to PR! And that's math.
  • Maria Droujkova   March 2, 2013, 7:05 a.m.
    In Reply To:   Lisa Ritt   Feb. 24, 2013, 6:05 p.m.

    Lisa, here are some of the main math ideas Dogon people have, which I gleaned from the article. It's a research paper, so the language is dense and jargony. Here:

    • Infinitesimals (a calculus idea)
    • Powers of 2 (2, 4, 8, 16...) and the base two system underlying the world
    • Non-positional but power-based system of numbers (mande reckoning), for example, 80=(2^3)*(2*5) and 60=(2^2)*(3*5)
    • Spiral as an extended geometric metaphor of growth and development

    The big point is that the culture of Dogon has complex systems that can be expressed in terms of modern Western math, but are significantly different to be interesting and valuable even in the modern world.

  • Maria Droujkova   March 2, 2013, 7:14 a.m.
    In Reply To:   Lisa Ritt   Feb. 24, 2013, 7:04 p.m.

    Lisa, going by definitions you selected in Part 1, humanities already intersect with math in their "analytic" part. If you want to humanize numbers (nice turn of the phrase!) - you will want to include critical and speculative methods!

    One simple activity for young kids that I like a lot does just that, as I realized reading your comment. Wow, I never thought about it this way... What I do is ask kids to draw numbers as characters, and to tell their stories. What color are numbers? Do they have tails or wings? Which ones are kind and which ones are mean? What are some numbers you personally like, and what note would you play for those on the piano?

    I see how this activity adds critical and speculative approaches to numbers. Some kids spend hours and hours developing their numbers as heroes of stories, or drawing comics about them, roleplaying them and so on.

    (The picture did not insert into the post. You need to first upload the picture to the server using the image dialogue.)

  • Gina Mulranen   March 2, 2013, 10:47 p.m.
    In Reply To:   Maria Droujkova   March 2, 2013, 6:51 a.m.

    What an interesting course!! Thank you for that link. When reading about the introduction to the course, I was also thinking about one of the courses I teach. The 5th grade gifted math course I teach before the students get into Pre-Algebra is called "Foundations of Mathematical Thinking." One of the objectives of the course is to teach students the how and why algorithms work from multiplying mixed numbers to how the order of operations developed. I find that even when students come into this course saying they have already learned how to do all the computation, they are still learning new ways of looking at problems or having an ah-ha moment when"it all makes sense now!" I really enjoy this class because of those lightbulb moments and the depth at which I am able to take with each topic. I really think that when students start to think about math and how it all connects and works together, they will be more successful when learning and applying new concepts.

  • Katherine Hanisco   Feb. 20, 2013, 12:18 p.m.

    Hi all! Once again, I thought we had a great discussion today and I really enjoyed hearing everyone's different perspectives. I wanted to provide links to a couple things I mentioned in case anyone is interested in reading more.

    The Unreasonable Effectiveness of Mathematics - this concept is something that has fascinated me long before I knew there was a name for it. The way that mathematical models, which can often be derived so elegantly and neatly, can accurately describe the real world, which is often so messy, is one of my very favorite thing about mathematics.

    And here is an article that talks about the psychology of scientific theories. It was Richard Feynman who said it, but it was in reference to the Milikan oil drop experiment, not the Rutherford experiment as I said during the meeting. I think this is an interesting overlap between science and the humanities. As much as we want science to be objective, it is still important to take the time to examine the results in a psychological or cultural context.

  • Maria Droujkova   March 2, 2013, 7:16 a.m.
    In Reply To:   Katherine Hanisco   Feb. 20, 2013, 12:18 p.m.

    I am totally stealing (with attribution) the "unreasonable effectiveness of mathematics" term as a discussion prompt! Thanks for the links.

  • Gina Mulranen   Feb. 16, 2013, 10:08 p.m.

    Hi everyone!

    I just wanted to share my excitement about using the website that was suggested by one of the students in this class.

    Here are the links to the web pages that display all the Valentine's day messages my students created using the website. This was an extra credit assignment where they had to compose a poem or creative writing piece that incorporated the language of Valentine's day and explain a math concept they have learned so far this year. (Foundations) (Algebra 1) (Pre-Algebra)

    Thank you for sharing all these great resources! I am loving it!

  • Maria Droujkova   Feb. 18, 2013, 8:27 a.m.
    In Reply To:   Gina Mulranen   Feb. 16, 2013, 10:08 p.m.

    Gina, can I use some of these posters on my blog? With attribution, of course. What a neat project!

  • Gina Mulranen   Feb. 18, 2013, 8:04 p.m.
    In Reply To:   Maria Droujkova   Feb. 18, 2013, 8:27 a.m.

    Of course! I printed out the posters and hung them on my door for Valentine's Day. The English teachers were very impressed with the creativity connecting creative writing with math concepts. Glad you enjoyed it! I am happy to share!

  • SueSullivan   Feb. 16, 2013, 8:21 p.m.

    Dr. Droujkova - just wanted to give you 'props' for mentioning XKCD Comics!  

    I found them very funny and when I sent the link to my sons, they said it was all the rage in school (grades 10-12) and that you were "spot-on for knowing what students like".  You certainly know how to relate to people of all ages; I feel this is a critical part of being a good educator although coursework rarely mentions this.  Thanks for demonstrating another important aspect of teaching!

  • Maria Droujkova   Feb. 18, 2013, 8:23 a.m.
    In Reply To:   SueSullivan   Feb. 16, 2013, 8:21 p.m.

    Sue, thanks for the props. I also found that XKCD is one of my interests that I share with a lot of young people. Common interests are necessary: they help us to relate to one another, and to have deep and meaningful conversations. As an aside, I found gaming to be hugely helpful in that regard, as well.

    We had a curious discussion of the comics with my teen's friends. Turns out that in many ways, XKCD plays the role of those old-fashioned books introducing young people to the grown-up world: "Miss Manners" or "Young lady's primer" or such. I've had the comics in my blog reader subscription list for some years, and I noticed it has been addressing so many aspects young people need to know! How do you deal with pickup artists? What to do if your loved one has cancer? Why is it hard to pick a college major? (to the tune of "The Modern Major-General")

    There are two resources associated with XKCD that are very relevant to this course. First, it has an excellent, active math forum (and science, linguistic, etc. forums) where you can pose questions - or send your students to pose questions.

    Second, it has a wiki explaining math and science behind the comics. For example, this is the page explaining Zeno's paradox that comes up in this comic:

    The prosecution calls Gottfried Leibniz.

  • Katherine Hanisco   Feb. 20, 2013, 12:53 p.m.
    In Reply To:   SueSullivan   Feb. 16, 2013, 8:21 p.m.

    Sue, I completely agree about the importance of relating to students. I think it's easy for kids to see teachers as adults who are so far out of touch with their own lives that they just tune them out - I think someone (was it you?) mentioned the teacher from Charlie Brown saying, "wah wah wah-waaah wah." Having some common interests or experiences helps build rapport that works both ways in the classroom. It gives us as educators some insight into our students that we can use to help tailor material to their needs (this connects well to our Differentiation course readings!) and it also gives students the chance to see us as someone who isn't totally out of touch with their lives. I think coursework neglects to talk about this because it may seem like a minor thing that is not directly related to curriculum or assessment or anything like that, but I believe that establishing rapport and building trust and respect between teacher and student increases student engagement, and that can make a HUGE difference.

    Related to that, I think that it's also important not to stretch the truth about our interests just for the sake of relating to students. Kids are so smart when it comes to spotting adults trying to pretend they know about things they don't, so I think we need to find common ground in authentic ways. One I've been thinking about recently is how to incorporate sports, which is a common interest of students, into math classes. I don't know a single thing about sports, and so I don't know how to integrate it authentically into a lesson and if I tried to talk about it with students, it would take them about two seconds to realize that I have no idea what I'm talking about.

    And since we're on the subject of xkcd, here is one of my favorites (which is relevant to our discussion today!) laugh

  • SueSullivan   Feb. 20, 2013, 6:09 p.m.
    In Reply To:   Katherine Hanisco   Feb. 20, 2013, 12:53 p.m.


    Love the comic!

    I think referencing sports is a great idea, as you said so many students are involved directly (athetes) or indirectly (observers).  I don't think that you have to love sports (or be partcularly knowledgeable about them aside from the basics) in order to integrate them into a lesson.  Students often love to talk about their interests, and having a chance to 'teach the teacher' might be especially engaging.   For example, asking students to explain why a football goes farthest when thrown with a spiraling technique will give you the chance to learn how they think about it,  so you could fine-tune your physics discussion if needed.  Hockey fans could be lured into a discussion by asking them to explain (in their words) what determines the path a deflected puck will take.  And so on.

    I also look forwarding to reading the 'Unreasonable Effectiveness...' article - thanks so much for sharing your ideas and resources!

  • Katherine Hanisco   Feb. 21, 2013, 8:05 p.m.
    In Reply To:   SueSullivan   Feb. 20, 2013, 6:09 p.m.


    Great point about giving students the chance to be the expert and teach the teacher! That's a great way to get them engaged and integrate their interests into the material.