Week 2 Carnival of themes (January 23-29)


Please post responses to the task here, using the Post Comment button at the top right corner:

I put together themes you suggested for the course in this mind map: http://mind42.com/pub/mindmap?mid=994691af-7ac0-42ac-b297-0279be4568fa It was a fun task, and of course it's not the only way to summarize themes - questions and comments and versions are welcome. The whole task took about three hours, but comments may be much faster. Here's the bird's eye view on the map (too small to read).

This week's topic, "Scope of modern elementary mathematics," is "meta" - it fits with all our themes. This task is about us building a definition of what good modern elementary math is, with current examples. 

  1. Find six blog posts, forum discussions, videos, articles or any other online content that goes with your themes from last week, AND are examples of "modern elementary math." You can spread examples over themes (two per each) or distribute them any way. 
  2. Limit your search to fresh, current content - either something posted within the last few months, or something still currently under active discussion. Use time limits in your blog or web searches to do so. This will raise the chances of dialogues happening.
  3. Leave comments at places where you find examples, adding something to the theme (as expressed there).
  4. Copy all your comments and links to their web pages in one comment to this thread. You may want to copy comments and links into a document as you go along, because some places moderate comments (slowly!) and you won't see them for a while.

We will end up with something similar to a blog carnival, but not limited to blogs, and with our comments in it. Here is an example from the latest, 46th issue of "Math Teachers at Play" carnival by our Denise - the part about math puzzles:

  • Gary shares a few puzzles that elementary-age children can understand but adults can enjoy exploring as well: Numberplay: Tanton Wordless. [Errata: Moving your mouse over the second picture will display solutions for four of the six puzzles shown, implying that two are impossible --- but really, only one is impossible. Can you find the missing solution?]
  • My entry for the carnival is the 2012 Mathematics Game, a terrific puzzle for middle school and beyond.

Here is another example from the themed Mathematics and Multimedia carnival, by Murray Bourne and featuring Bon and Denise:

(1) Bon Crowder of Math is not a Four Letter Word has written an interesting thought piece on the difference between motivating and inspiring students, in:

Are You Teaching Math Through Motivation or Inspiration?

(2) Denise in Let’s Play Math! says “Let’s look at two common mental models — partitive division and measurement division — to see how the sister could have divided her pie…” in:

How to Understand Fraction Division

(3) Colleen Young (who has a “keen interest in how new technologies can deepen the learning experience for students”) has begun a new blog aimed at students. She’s right – most math blogs preach to the choir – it’s about time there were more blogs addressed to students.

Hello Students!

(4) And finally in this section, here are my suggestions (right here insquareCircleZ) on:

How to make math class interesting?

Task Discussion


  • Keisha   19 februari 2012 21:57

     

    1. The first blog I found is about learning Math through play. This blog is really cool because blogger that started it uses domino pieces for Math with little kids. I never thought about using dominoes with kids. She makes a great point too about how it helps with their fine motor skills. The dots on the dominoes are used for addition and the different colors on them help for visual appeal.

    http://www.dreambox.com/blog/learning-math-through-play-from-guest-blogger-dawn-morris

    2. I think this is my favorite find out of all these. This article is about teaching/learning math through dance. Me being a dancer I was so happy to see this. Two guys came up with a way to cater to people that are kinesthetic learners. There's a video in the article that shows you a short clip of Erik Stern and Karl Schaffer, the founders of Math Dance, teaching teachers how to combine Math and Dance. Teachers commented in the article that have done Math dance saying that they saw students improve in math from it. Since I love to dance I'm definitly going to try this.

    http://www.sciencedaily.com/videos/2008/0503-do_the_math_dance.htm

    3. This blog is about learning math through music. The general topic is about if listening to music at a young age will increase your mathematical abilities. I've heard that if you're pregnant and play classical music it will make the baby smarter. I always thought that it was not possible but after reading a lot research over the years I do think that it plays a role in helping the brain process information. In the comments I was reading someone posted that when her students use music to summarize what they learned or are introduced with a subject through song they learn better. I usually you make up songs to help me study so I don't doubt for a fact that this works.

    http://serendip.brynmawr.edu/exchange/node/1869

    4. This next blog I found is about learning math through play. What better way to teach math to kids than to have them play engaging games that require counting and pattern recognition. This blog site gives you games that wiil be popular with kids. One of which never crossed my mind for some reason. It's number two on the list and its cash register. When I was little I play 'Market' and other random games that required a register. I think a lot of kids still play this game now and having fake money to use and having them actually count the money to give you the right amount is cool way to learn math.

    http://simplehomeschool.net/learning-math-through-play/

    5. I found a video about teaching kids math with computers. I would think that using computers at a young age will be distracting for kids and maybe even hard for them. After listening to the video I think it's a great idea. Using technology is a part of our lifestyle nowadays so introducing it to young kids it's not a bad idea. The speaker makes a great point about how teaching kids to count with their hands can be tedious at times. We only have ten fingers so to go beyond ten can at times be hard for them to do. Reading the comments on the video people seem to learn better when using computers.

    http://www.youtube.com/watch?v=60OVlfAUPJg

    6. This video is about teaching the magic in math. The video is about an Elementary school that integrated math through all subject areas and saw a big improvement in their test scores. I don't remember having math integrated in all subjects in my school. I think that I would have improved in math earlier than I did if they did this. I love the strategies the teachers use to get the students to talk their way through problems. They call it discourse, they have the students talk to one another to come up with a solution. I think I saw this at one of my field works and the kids seem to love sharing ideas and opinons to come up with an answer.

    http://www.youtube.com/watch?v=E91gAjunqOM

  • Amanda Graf   29 januari 2012 15:18

    Modern Kinesthetic:

    http://www.youtube.com/watch?v=1-AEqtUihnE&feature=fvsr

    Motion in learning is a great way to keep the attention and interest of students. Movement is very important in the classroom. It keeps the body and brain awake. Sitting in a desk listening to a teacher talk all day is not very beneficial to a student. Kinesthetic learning aids in a student’s memorization of the material they are learning. I found this video on youtube and I think the theory behind it is genius. I do think that this particular rendition of the lesson is ridiculous and poorly done, but I think the lesson itself is great. It prompts a child to hop on a trampoline x amount of times on the left foot and x amount of times on the right. It then asks the child how many times in total he or she jumped. I think it’s a great combination of movement and math and is something that would amuse the students as well as teach them addition.

     

     

    http://www.mindsinmotion.org/creative.html

    This is just an article I found that is one teacher describing their experiences and opinion on a Kinesthetic approach to teaching. She explains the importance and benefits of movement and dance in the classroom. At the pre-school I work at, we had one of the classrooms go into the gym and split them into groups and assigned them each a number and told them to lay on the floor and create that number using their bodies. This was a lesson plan suitable for a pre-school class of 3 and 4 year olds, obviously it would be too simple for an older class, but it could be adjusted to be suitable for older students as well. They really had to rely on team work to figure out how to build their number, the teachers would not assist them in the process. In the end, they were all successful and they loved doing it. We took pictures of all the groups in their number formations and after that, writing numbers was easier for them because they associated it with the group activity. When they have to write the number “4,” for example, they remember that was the one where Kaylie horizontally connected Kyle and Dylan, who were laying vertically head to head, and Mackenzie who was on the other side, also laying vertically.

     

     

     

     

    Modern Visual:

    http://www.youtube.com/watch?v=O__iSFa_0T4

    While researching some modern forms of visual mathematics, I discovered a learning program called enVision and thought this program seemed extremely affective. It utilizes different visual methods to teach elementary-age students. I loved that the program not only consisted of text books, but also computer programs and SmartBoard programs. The program also prompted the students to use 3D objects to learn with. For example, the video shows students using blocks to learn fractions. EnVision is offered for different grade levels and they all seem age appropriate. None of the videos, games and computer programs seemed too childish for the grade level it was designed for. EnVision seems like a GREAT source for a visual approach to teaching elementary math.

     

     

    http://www2.tech.purdue.edu/cgt/I3/SMILE/522-054.pdf

    Although Sign Language has been around very long before the 21st Century, it has become a more modern trend to teach it in elementary school classrooms. Recent research has come to the conclusion that Sign Language isn’t only a means of speaking for those who are deaf. It is also a visual approach to communication and learning that appeals to a lot of students, deaf or not. Sign Language is taught as a second language in all of the classrooms at the school I work at and it is picked up very easily by most children. There are children as young as 14 months that can identify colors and speak them in Sign Language. Math is a tricky subject for a lot of students, and learning it through sign language is sometimes easier for them, I’ve noticed. This article discusses a web program for kids that teaches math in ASL. Although the first paragraph of the article expresses the importance of this program for deaf children, it is the opinion of many that kids without any hearing disabilities would also benefit from using this program.

     

     

     

    Modern Auditory:

    http://www.youtube.com/watch?v=v9dx2o7m6GI

    Songs are a great teaching method for auditory students. The Kindergarten class that I work with could name the 50 states within the first week of the school year because we taught it to them as a song. They can count easily to 100, count by 1's, 2's, 3's, 10's, and to 10 in Chinese and Spanish. They picked this up so easily because we, as the teachers, reinforce the day’s lesson plan with songs. Songs appeal to most children, even if they aren’t primarily auditory learners. While searching the Internet for a good math song, I came across this pirate song and thought it was great. It was even stuck in my head after listening to it just once! I think it’s modern because kids these days aren’t into the same things I was in, growing up in the 90s. They don’t find Sesame Street as appealing as I once did. Kids want whats “cool” and, especially for the boys, themes such as pirates are what is cool. Since I was confident that the song would hold the attention of the students, I paid attention to it’s content, which I was also impressed by. I think it taught basic subtraction in a fun catchy way. Like I said, it was stuck in my head, and I think it would stick with kids as well. When it comes to auditory learning, finding songs that are catchy, “edgy” enough for 21st Century kids, and educational can be difficult but very effective!

     

    http://www.riverspringscharter.org/elementary-k-6/curriculum/learning-resources/learning-styles/Auditory-learners

    I found this page to be really interesting because it lists various things a teacher can do to accommodate a student who is an Auditory learner. One thing I found interesting on here was that it suggests giving a student headphones with quiet music playing while they are taking tests or doing work to be white noise and block out any auditory distractions that may be happening in the classroom around them and distracting them from their work. I, personally, could never do this, I need dead silence when I work, but I feel that this would be really helpful for a lot of students.

     

     

     

     

     

  • Maria Droujkova   30 januari 2012 06:15
    Reageer op:   Amanda Graf   29 januari 2012 15:18

    Amanda,

    Thank you for examples from your experiences. You may want to leave them as comments in the places you found, so authors of videos and posts can benefit too (just be careful about the words chosen for criticism). 

    Here are the aspects of modern elementary mathematics I see you bringing up:

    • Kinesthetic learning
    • Team work
    • Visualization, visual learning
    • Use of signs and gestures for babies, sighted older kids, everybody (we did baby signs as a family, too)
    • Using catchy, edgy, cool content, especially catchy songs
    • Modifying your auditory environment to suit your preferences and needs (silence, background music, white noise, nature sounds, etc.)
  • Kathy Cianciola   8 februari 2012 10:31
    Reageer op:   Amanda Graf   29 januari 2012 15:18

    Hi Amanda,

    I just watched "Trampoline Math."  I agree that the idea of counting jumps, and using movement in the study of math is a great idea, especially since children are so highly energetic. I also agree that the lesson could have been done more effectively.  Most children would probably prefer to jump one hundred times rather than three or four.  Why not keep on jumping!  I think that a music CD about numbers would really boost this activity.  Incorporating stretching and clapping into the activity would also be great since these are all things kids love to do.  The video really had me thinking about ways of making this work in a room with 25 students.  I guess 25 trampolines in a classroom could be seen as eccentric, but it would sure be exciting for the children. Perhaps just jumping on pretend trampolines would work.  What do you think?  

  • Carolyn   28 januari 2012 14:36

     

    http://crisscrossapplesauce.typepad.com/blog/math-problemsolving.html

     

    This blog I found off of http://www.kindergartenkindergarten.com/ the site at first seemed just to be a teacher’s outlet for her endless thinking, but I still combed through it and found this blog about problem solving. Her method is exactly what I did as a kid. She talks about math problem solving as almost a journey; there are many ways to one end. I LOVE this philosophy. Everyone always says math is so cut and dry, there is only one answer, 2+2=4, however the beauty in math is how you come up with that answer. The teacher on this blog uses a method called share and compare with her students, who are kindergarteners, to solve problems. I admire her persistence with this process, as with kindergarteners nothing is easy. The process involves a warm up problem, a problem of the day, sharing solutions, and then comparing them. A simple process like this I think would work great at the beginning of each day or math lesson to warm up the kids to that days activity and also to let them explore different routes (problem solving skills) to their end journey (solution).

     

    http://www.blog.republicofmath.com/archives/4834

     

    Republic of Mathematics I found is a great resource for different problems and solutions, but also for posts like the one above. The link above will take you to a blog about testing. Although this was not one of my 3 themes, it is something I feel strongly about. The entire blog questions the effect tests have on students and whether or not they should be used. My favorite part of the blog is the last part titled, “Should we use tests?” I think his answer describes exactly how I feel about test not only as a pre-service teacher but also as a student, what are tests exactly measuring? I loved the part in the blog when he said that one thing we can be sure tests do is that they measure each student against their classmates on that particular task. Frankly, I think that is all tests do.

     

    http://www.dreambox.com/blog/learning-math-through-play-from-guest-blogger-dawn-morris

     

    Learning through play has been a constant theme for me this school year. I took an early childhood class last semester and learned how pre-school is not just playtime, but that the kids are actually learning too. This blog supports that idea of playing, specifically through math. The blog demonstrates math through play with dominos, something I never used mathematically as a kid. However the first paragraph of the blog explains those little zigzag trains that most of us probably made at one point during our childhood. The one where you stand the dominos up next to each other, just far enough apart so that when one falls it will hit the one in front of it. She concludes by saying this helps develop spatial skills. The more and more I began thinking about dominos the more ways I came up with to facilitate math skills. One particular skill is math families. Dominos are an easy manipulative for children to use to add numbers. 1+2+4=5 and if you mix up the numbers the sum is still the same.  Therefore whether or not you use the dominos mathematically, children are learning from them.

     

     

    http://mathematicslearning.blogspot.com/2011/09/teaching-math-through-games.html

     

    Teaching math through games is the focal point of this blog. The simple task of rearranging the room to play math games is a math task in itself. For young children rearranging the room into a rectangle or into a triangle lets them practice their shapes, but indirectly. My qualms with testing are only furthered here. Kids don’t always need a test for a teacher to assess them. Tasks such as rearranging desks into shapes are an informal way of assessing their knowledge. The rest of the blog provides different math games that allow students to develop math skills along with social skills by working together.

     

    http://mathfour.com/patterns/finding-patterns-in-a-lokta-paper-blank-book

    http://mathfour.com/patterns/teaching-patterns-with-playful-bath-shapes

     

    I believe patterns are something that are found everywhere in math and therefore it is important to foster the idea of patterns starting at a young age. Both of these blogs, which I noticed Bon has a part in (Thanks!), deal with patterns. The second one supports my theory that patterns should be taught at a young age and can be. Simple bathtub toys can be categorized into groups, all blues together, all boats together. This can obviously be done outside of the bathtub with regular toys or in a classroom with marbles, erasers or whatever the teacher may have on hand. The first blog furthers this idea of patterns and the fat that they are everywhere, including the notebook that she bought. Obviously when she begins talking about slope, the activity is meant for older students. However I think with deeper thinking a teacher could buy an assortment of items that she can identify at least one pattern from and use it as an activity. Give an item to a group or each student and have them find a pattern. This would be learning through play also. 

  • Maria Droujkova   30 januari 2012 06:30
    Reageer op:   Carolyn   28 januari 2012 14:36

    Carolyn, great connections there - I like your trains of thoughts that lead to designing tasks, like dominos. One reason we read one another's blogs is to get that process going. I'd like to encourage you to post your comments, or parts of them past the intro about the blog, in these places, too - the authors would love it.

    Here are aspects of modern elementary mathematics I see in your stories:

    • Explore, compare and contrast, share different routes in problem-solving
    • Quest for better tests, and the question if the best test is no test
    • Learning through play, math games
    • Introducing deep math concepts (such as patterns) at very young age
  • Carolyn Lesser   26 januari 2012 16:45

     

    On this website I found some information to back up that playing games can really improve math skills. This particular article talks about the benefits of board games. "The researchers, Robert S. Siegler and Geetha B. Ramani, designed an activity resembling the popular board game Chutes and Ladders, in which they had 124 pupils count and move pieces along numbered squares. All the preschoolers tested were from families that participated in the federal Head Start program, which serves children from impoverished backgrounds." They played the game numerous times over a two week span and there was a great improvement in their math skills. The article says that by teachers allowing their students to play board games in class they are helping the disadvantaged students who do not have those kinds of luxuries at home. I wasn’t able to find a comment box but I emailed the site this: “This is a wonderful study! I was wondering if there are any other games out there that are having the success rate of A Great Race?”

    http://eclkc.ohs.acf.hhs.gov/hslc/tta-system/family/For%20Parents/Everyday%20Parenting/Parents%20as%20Teachers/PlayingGamesin.htm

     

    This article promotes problem solving skills in elementary math. It lists many ideas to help a teacher create the classroom for an environment conducive to teachingthese skills and even provides another link to read more about it: http://mathforum.org. They list strategies for three main large ideas and then branch off in to more specific groups. The three main ideas are promoting discourse, focusing on language, and using small and large group teaching strategies. It helped to see why problem solving is so important and ways that I could easily teach it in the classroom. Here are my comments: "You have many great ideas for problem solving skills! I excited to test these ideas out when I have my own classroom. What do you find is the most crucial key to teaching problem solving skills and what do students most struggle with in this process?”  

    http://teachingtoday.glencoe.com/howtoarticles/promoting-problem-solving-skills-in-elementary-mathematics

     

    In this article a teacher talks about how she uses games to help excite her students to learn math. Not only do the students above or on grade level enjoy them but so do the students that are at risk. She wants these games and hands on activities to help them like math more than they did in the beginning of the year. They feel excited and accomplished when they complete the game or puzzle that are given and are always asking to for more. She also mentions that these games can promote problem solving which is another one of my themes. This particular teacher is using a brand of games class Think Fun Games. She also had other game stations in her classroom for navigation, shapes, and brainteasers. Here is my comment: “This is a wonderful way for students to learn math! I was wondering what your success rate was with children that were at risk? Also does a particular game seem to be more helpful than others?”

    http://www.thinkfun.com/node/73

     

    This website I discovered is fun and very useful! One particular blog on the site was about measurement. The blogger posted great word wall visuals and words all about different measurements. The pictures are great and I can tell they will really help students remember what each word means. I am terrible at remembering these things even now and the pictures have helped me. It is easy enough to print out or to make your own pictures and just post them up in your classroom. Here was my comment: “This is great! How successful has this been for everyone? Also what age groups would be most appropriate for this word wall?”

    http://www.guided-math.com/2011/11/measurement-word-wall-posters.html

     

    I searched Youtube for some interesting videos and found a series of games. They are called expertvillage and are all different games from learning shapes to counting money. The video I chose was on learning math operations. This was my comment: “This is a great game! What age groups would suggest this game for? Also do you have any kind of a success rate with your games and if so which normally seem most successful?”

    http://www.youtube.com/watch?v=FtD-6mUShdA&feature=relmfu&ytsession=xUFh3UvcFS1OcJwbSGr6tQIesqfBNKsQIh6cKS0RnSORnptmil7KNSGuCBW7SlXr9pA-b4dE6vNPW52_x-8O_d3qWre0DMrmbSTdXEw8zHml6oQUcQxdx1hnkH8-oEKuqr5erjaN_jLSL10fNkeJ1t4K5wgg5SVcnvRIjRz7gbdJn7qBuKtYWTlS2A21ehWy1F39Ir-Ax_6bfo2CktKwZRv_Aw1N4PNIilbdaMNk7Rz8VlJ5DKlyoihLxJHmx1LcqfbaZmkFH-1ceLtHZDanrHspmqtfUjVzOd3FGpzYiHA

     

    The last website I looked at is wonderful though it isn’t strictly just math. It is mostly science but it includes my theme of measurement as well and I strongly believe in integrating subjects so I thought it was perfect. It is called Foss and is very popular with teachers. They are kits for students over a period of time and are offered for all grades. The website is for parents and students as well. I was interested in the measurement games and vocabulary that was offered for the students. I emailed the website this: “I am a huge fan of your site and would love to know how much success you get from your online website. What are the most popular sections for students?”

    http://fossweb.com/modules3-6/Measurement/index.html

  • Maria Droujkova   30 januari 2012 06:47
    Reageer op:   Carolyn Lesser   26 januari 2012 16:45

    Carolyn,

    Glad you found the sites you liked and left them comments - people need to know what others think of their work! You are asking thoughtful questions, and I hope you get some replies. I prefer blogs that reply to visitors, but sometimes people get busy.

    Here are aspects of modern elementary math I see in your comments:

    • Learning through play, games
    • Problem-solving and its parts (e.g., attention to math language)
    • Research into effectiveness of learning methods
    • Using visuals to help understanding and memory
    • Integrating subjects (e.g., math and science)

    We'll continue working on the aspects this week.

  • Kathy Cianciola   25 januari 2012 23:35

    Here's a another great hands-on activity involvong a clothesline/ numberline.  The teacher strings a line up across the room, then the children are given colorful note cards with numbers written on them. They clip up their number cards with clothes pins, where they think the cards should go on the clothesline/ numberliine. The teacher can  also hang up a few baseline cards first, to give the children a reference point.   I think this is a great classroom math activity because the children are actively participating, and it's always a plus to be able to teach great skills while also giving everyone a opportunity to get out of their seats a move around.  I also clicked on another link on the same sight that shows a teacher who hung a string of Christmas lights across the classroom using it as a number line.  He pointed out that he had the children make use color patterns in the "light" activity.

    http://www.smartfirstgraders.com/number-line.html

  • SandyG   26 januari 2012 06:23
    Reageer op:   Kathy Cianciola   25 januari 2012 23:35

    I think I saw the same video with the teacher who used Christmas lights as well. 

    http://youtu.be/CP6bsrc5sH0

  • Maria Droujkova   30 januari 2012 06:56
    Reageer op:   Kathy Cianciola   25 januari 2012 23:35

    Kathy,

    Thank you for examples you found, and for comments you left for other participants on this page. I am replying to all your comments in one message, for ease of indexing. Here are aspects of modern elementary math I found in your stories:

    • Active participation of everybody
    • Kinesthetic learning through the whole body, moving around
    • Hands-on activities
    • Using computers and technology in general
  • Dinesh Tantri   30 januari 2012 13:38
    Reageer op:   Kathy Cianciola   25 januari 2012 23:35

    Inspired by this comment, I tried a variant of the christmas lights activity by writing numbers on the floor [ a digit in every tile ] and did a number of activities like " What comes next?" - I used cloth pegs to create patterns - We scaffolded everything we had to do in a great story with characters that appeal to my kid - So while he was out on this mission to save his favorite toy he had to do a number of things like figuring out "What comes next?" [ color or number ] or hop in twos etc.,

    Not quite sure why the photo rotated

  • Maria Droujkova   1 februari 2012 10:51
    Reageer op:   Dinesh Tantri   30 januari 2012 13:38

    Dinesh, thank you for sharing! This picture just says "Focused kid!" to me - he looks so engaged! 

    An aspect of modern elementary math that comes up in your activity:

    • Use of grand stories with characters, being on a mission, and roleplay
  • Carolyn   25 januari 2012 20:39

    I don't really understand part 3 and 4 of this task. Also do most people find blogs by just googling or are there popular websites where different blogs can be found? I am not all that familiar with blogging so if anyone could help that wouldn't be greatly appreciated! Thanks. 

  • SandyG   25 januari 2012 20:58
    Reageer op:   Carolyn   25 januari 2012 20:39

    Carolyn, Some of the blogs I found by typing "math blogs" or "elementary math blogs" or "special ed blogs_math" in my browser.  I also went to some of the results I got from that and followed links to other sites.  To get my 6 sites, I looked at a lot of websites!  I'm sure there is an easier way, but I read a lot of interesting information finding my sources.

    Not all sites allow you to post a comment, and I found that on the ones that did, most comments were just positve reinforcements (Great job! or Looks good!), but toward the bottom, you will sometimes see a place to post a comment. For part 4, I think it's asking us to include the link (copy and paste from your webaddress bar), and if you do comment, include what you posted on the blogsite in the summary you post for all of us to read.  Hope that helps!

  • Kathy Cianciola   25 januari 2012 23:40
    Reageer op:   Carolyn   25 januari 2012 20:39

    I have been finding mine through typing key words into Google.

  • Kathy Cianciola   25 januari 2012 19:40

    http://www.cmhoustonblog.org/2011/12/30/party-hat-symmetry/

    I have always loved creating 6-point snowflakes, and recently I've been making them with my son. I thought that this hat-making lesson would be a good hands-on project and a great lesson in symmetry.

     

     

  • Laura Haeberle   24 januari 2012 21:24

    Teaching Math Through Art:

    One interesting blog post I found was on a blog by Patrick Honner, an NYC math teacher. Honner was discussing a recent lecture by Craig Kaplan, a professor at Waterloo University. During the lecture, Kaplan discussed the presence of math in art, and the intricate examples all around us. I was most interested in the activity following the lecture, when the audience was split up into groups at various tables. They used “some tape, some scissors, and some clever mathematics” to create tiles on their table, which all formed together in a pattern. After reading the article, I thought of how this type of activity could be used in an elementary school setting, and could foster teamwork while teaching patterns. I commented:  Wow, that seems like a fascinating talk! Kaplan sounds like a brilliant man. I'm wondering if the table activity could be used for young students, as well. I could see it being done in an Elementary classroom, to help teach patterns and show more of a creative, artistic side to math!

    http://mrhonner.com/2012/01/05/math-encounters-craig-kaplan-on-math-and-art/

     

    I also found an example of a lesson plan that thoroughly integrates math and art. It’s titled “Symmetry Penguins” and was done with a fourth grade class. Mrs. Haake provided photos of the artwork created, which exemplified transformations and reflections of plane figures. The cut-outs were all penguins in scarves, so it seemed like a really cute seasonal activity. The art aspect was “complex symmetrical folding and cutting” and the math standard was “identifying, predicting, and describing transformations.” There wasn’t an area to comment, so I messaged the teacher : This sounds like such a fun activity! I like that you point out the standards that the children are meeting; it makes them more aware of what their learning process is. Could you tell me more about how the actual lesson went? What did the children enjoy? Were there any struggles through the process? Thanks so much!

    http://apexart.blogspot.com/2012/01/mixing-math-and-art.html

     

    Teaching Time:

    I even found a blog post that discussed two of my themes: telling time and technology. Jennifer Bogart, a homeschooling mom, wrote a post on an interesting iPhone app that she discovered, called “Jungle Time.” The app is aimed for young children learning to tell time, and features jungle animals and fun games to teach children these valuable skills. While reading, I was reminded of how much children rely on technology for learning. It’s incredible to consider the resources available now, and I’m sure that children would appreciate learning from the comfort of an iPhone. I commented: This sounds like a great app for any struggling students. I can imagine kids playing this over and over again without even realizing that they’re learning! Have you found many apps that you use while homeschooling? It seems like apps have the potential to be a very helpful tool.

     

    http://www.readingkingdom.com/blog/2012/01/18/add-math-app-your-homeschooling-curriculum-learning-numbers-telling-time/

     

    Another blog found also incorporated technology into the teaching of time. The post, written by a principal in Ontario, Canada, explained a bit about why children have such a difficulty with telling time. He talked about how much Canadian students had been struggling, and gave the details of a study trying to improve their time skills. In the study, a group of students in grades 1-3 were taught time through Mathletics, a website with fun math games. The study showed that their ability to tell time increased up to 40%, after using the site. I was pretty amazed at the statistics, and commented: I can’t believe how great of a tool Mathletics is. I’m wondering if the 1st graders had a larger achievement gap because of their young age or their ability to learn through Mathletics and other similar websites. Either way, it’s great that this type of technology is available in the classroom!

    http://blog.mathletics.com/index.php/2012/01/18/research-mathletics-in-the-classroom/

     

    Math & Technology:

    I was really happy to find Richard Byrne’s blog “Free Technology for Teachers.” This seems like the type of resource I’ll be able to use in the future, considering my theme on math and technology. Byrne posted two Youtube videos on teaching PEMDAS, both of which were catchy songs/raps. I can see how helpful it would be to use these in the classroom, since it sounds like something the kids would enjoy. Plus, it never hurts to have PEMDAS stuck in your head! I commented: This is a fantastic resource. Do you have any suggestions for how to implements these videos into a lesson on PEMDAS? For example, would you show the video at the beginning (to get everyone’s attention) or the end (to keep it fresh in their minds)? Hopefully they will come out with new and even better math videos!

    http://www.freetech4teachers.com/2012/01/pemdas-math-rap.html

     

    Another article discussed the difficulties of teaching math in the modern age. The author, Jon Ginsburg, insists that children become more stressed out when taking “traditional” tests, as the information is not at the touch of a button. These were things I hadn’t really considered when considering how to combine math and technology. Clearly, I’ll need to make it a smooth transition, so as not to overwhelm students when going from a math computer game to a multiplication drill. My comment was: Technology sure is changing the way that teachers need to approach their students. I feel like things are becoming more and more technology-heavy, and students grow up expecting teachers to be fully tech-savvy. It’s tough to incorporate technology, while still teaching the basics. Do you have any suggestions? Thanks in advance.

    http://audio-mastering-ebook.com/teaching-basic-mathematics-in-an-age-of-technology-practice/

  • Maria Droujkova   25 januari 2012 19:14
    Reageer op:   Laura Haeberle   24 januari 2012 21:24

    I've been doing "math arts" with young kids and, you can guess, they love it. Origami, snowflakes, 3d sculptures, computer art - and yes, somehow most of it has only been connected to math and math education in the last 10-20 years or so. Origami is ancient, for example, but Huzita-Hatori axioms were only formulated in the 90s. 

    Here is how I summarize aspects of modern elementary math that come from your stories. Does this summary work?

     

    • Math in art
    • Helping children be more aware of their learning processes
    • "Learning from the comfort of an iPhone"
    • Using statistical analysis of learning success (Laura's example was both about technology itself, and analyzing its results)
    • Using videos in lessons (purposefully, with planning)
    • Tension between computer-based learning (to which kids are used), and non-computer math tasks
  • Kathy Cianciola   25 januari 2012 20:16
    Reageer op:   Laura Haeberle   24 januari 2012 21:24

     

    Laura,

    I like the symmetry penguins.  I would love to know how they were created. Did the article share the process?

  • SandyG   24 januari 2012 17:15

    1. Number Sense

    My first theme from last week was number sense.  I found a really great blog written by a kindergarten teacher called Kindergarten Works, http://www.kindergartenworks.com/2011/08/monster-numbers.html. The blogger discusses her ideas for number sense by sharing some materials that she developed. She developed a plan to help children learn how to write numbers, but she approaches it through rhyme.  This fits in perfectly with my belief that many children learn concepts easily through rhyme, song, and mnemonics.  I told her, “I think this is a great way to approach the subject.  Offering children easy to remember sayings as a way to remember the way to write numbers is a great approach.  Well done!” 

    Another site called Smart First Graders.com also discusses ideas for introducing numbers in a way that makes them relatable for students. This specific blog page  http://www.smartfirstgraders.com/number-sense-activities.htmlincludes the idea of looking for times and places throughout the day to practice counting.  I think this is a great idea.  Walking down the hall counting steps can be both fun and educational.  I can imagine handing out papers or other materials and asking students to count.  Students can count the number of people buying lunch or packing.  There are an abundance of opportunities during the day to count. The page states, “There is no better teacher than repetition”, and I believe that (Number sense activities, 2011).   

    2. Teaching math in a way that is exciting and not intimidating.

    Researching my second theme of teaching math in a fun, non-intimidating way, led me to a blog carnival called Let’s Play Math! athttp://letsplaymath.net/. One of the links led me to a kids’ activities blog. One mom used something as simple as an egg carton to develop a game she calls Egg-0.  She says, “Hands-on math games are a great way to add variety to your child’s education…not to mention a fun way to practice math facts!” (Heather, 2011)  I agree.  Many children learn better by changing concepts from abstract to hands-on.  I am most familiar with the use of manipulatives in a special education setting, but certainly it could be beneficial for all learners.  Using an egg carton and writing numbers in each cup, the mother had her place two buttons in the carton, close it, and shake.  The child opened the carton and would either add the two numbers together or subtract them depending on what they were practicing.  Fun and educational—you can’t beat that!  I told Quirky Mamma, “This is a great idea!  I think the use of manipulatives, or anything that can be "hands on" and fun will help kids learn.  This could be used for so many different concepts and not only for numbers but letters as well”.  I can also see this working for number identification and comparisons such as greater than or less than. 

    I think using technology can change something as mundane as flash cards into a more interesting, interactive experience for children.  There are many online flashcard sites, but I came across Mr. Martini’s Classroom at http://www.thegreatmartinicompany.com/.  It’s colorful, easy to use, and makes practicing more fun. I can see a site like this used in conjunction with “old fashioned” flashcards.  The site includes activities for pre-K through 7thgrade.  The pre-k link includes shape identification and counting to ten.  Certainly, though, I find a flaw in that a pre-K child would not be able to read the flashcard to answer the question.  There is a voice reader icon, but the voice is very mechanical and speaks quite quickly.  Still, with the help of an adult, a child could work through the site, and it would give the child some practice using technology.  I sent a comment to Mr. Martini: Your site is very extensive and including printables is great! I can certainly see using your site as a way to reinforce concepts.  I am certain that children enjoy working with the computer, and it is a way to practice that is certainly entertaining. 

    3. Reaching special learners

    The website http://www.paulabliss.com/math.htmoffers a lot of information about teaching math to students with disabilities.  It includes suggestions such as different presentation options and response options.  An example of a presentation option includes presenting a problem using physical objects or manipulatives.  The site also includes a great section about the way different weaknesses in information processing may affect math performance.  For example, a student with visual-spatial deficits may have trouble telling numbers apart, using a number line, or even knowing in which direction to read numbers. A student with a deficit in memory skills may have trouble retaining information, making connections to previously learned material, or telling time.  Each area of deficit can present challenges in different areas, and it’s important to keep in mind that a struggling student may have an undiagnosed challenge that requires special attention.  The website also includes different accommodations for various specific learning disabilities.  

    On Teaching Learners with Multiple Special Needs http://teachinglearnerswithmultipleneeds.blogspot.com/, I found an interactive tool for teaching numbers. If you scroll down, you will see it. Each page contains a “jumble” of numbers.  The instructions give possible ways to use the tool including finding the numbers in order, matching, and a few other ways.  This tool would also be helpful for students who have vision difficulties and may need practice scanning a page. For teachers of special education, this blog offers a variety of lesson materials and suggestions-- not only math related. 

    I sent a message to the blogger: This numbers book can be used in a number of ways.  As a way to encourage children to visually scan a field, it could allow for a bit of vision therapy at the same time that it reinforces number recognition.  I like that technology allows us to offer this exercise in a way that is both eye-catching and educational.

     

    Number sense activities. (2011). Retrieved January 2011, from Smart First Graders: http://www.smartfirstgraders.com/number-sense-activities.html

    Heather. (2011, December 28). Make your own math games: Egg-O. Retrieved January 2012, from Quirky Momma: http://kidsactivitiesblog.com/make-your-own-math-games-egg-o/comment-page-1/#comment-28531

  • Maria Droujkova   25 januari 2012 18:58
    Reageer op:   SandyG   24 januari 2012 17:15

    Sweet list, Sandy! The creator of Let's Play Math, Denise, is a participant in this course. 

    Here's how I would summarize aspects of modern elementary math your examples bring up. Does it make sense to you? What would you change in the summary?

     

    • Using psychological tools such as mnemonics and rhymes
    • Integrating learning into daily routines in little chunks
    • Hands-on work, manipulatives
    • Using technology to spice up routine work and make it interactive
    • Different presentation options, based on individual student's information processing features
    • Using interactive tools for focused training, such as scanning games (vision therapy)
  • SandyG   25 januari 2012 19:11
    Reageer op:   Maria Droujkova   25 januari 2012 18:58

    Your summarization list does make sense, and includes everything that I think is so important in trying to differentiate instruction to meet students' learning differences.  Reading it so straight forward in your list really made me say "Wow"!  Maybe teaching math doesn't have to be like trying to teach a language I don't speak.  Maybe the concepts are different, but good techniques are what makes a teacher successful.

  • Maria Droujkova   25 januari 2012 19:20
    Reageer op:   SandyG   25 januari 2012 19:11

    You touched a very big conversation, that often grows into arguments or even skirmishes in "math wars" - namely, the balance between general techniques for helping children learn and particular content knowledge of a subject.

    To take your example: is it possible to help a child learn a language you don't know at all, and to do it well?

  • SandyG   25 januari 2012 19:56
    Reageer op:   Maria Droujkova   25 januari 2012 19:20

    Good question.  I think technique has to be there-- regardless of the subject.  We've all had teachers who didn't have the skill necessary to deliver a lesson effectively.  Did the teacher know the subject?  Sure. However, I think that the ability to deliver the information appropriately for the target audience is extremely important, and if the receipt of the information by the student is impeded in anyway, either through their own barriers or because of an ineffectual delivery, then learning will not be as complete as it could have been. 

    Can you help a child learn a language that you don't know?  Sure. If you're willing to learn along with the child.  Can you do it well?  Hmmm. Certainly not as well as someone who is learned in that language. If the teacher is motivated, though, and willing to hit the books, is able to find the right resources, and accepts that it will require a lot of work, then I think there's a chance it could be a productive lesson.  The reality is, right or wrong, there are a lot of non-math lovers teaching math lessons in elementary schools. It would be great if there were math specialists available to teach all of the classes in every elementary school, but at least where I live, the classroom teachers tackle all subjects.    

  • SandyG   24 januari 2012 17:04

    Do we post our assignment here or send it through googledocs?

  • Maria Droujkova   24 januari 2012 17:08
    Reageer op:   SandyG   24 januari 2012 17:04
  • Kathy Cianciola   24 januari 2012 14:39

    Hi Bon,

    I'm not sure either, but since this seems to be the year of Technology I think I may try to do some math activity that can be done on the computer.  Since we are supposed to design it, I may find this rather challenging. Maybe I will create something in a paint program on my PC.

    Kathy

  • SandyG   24 januari 2012 16:02
    Reageer op:   Kathy Cianciola   24 januari 2012 14:39

    I, too, assumed that modern would include some technology integration.  We have to design an activity, but I took that to mean it can incorporate a tool that may already be out there such as Study Island or any number of iPad apps.

  • Bon Crowder   24 januari 2012 10:41

    I don't have any idea what it means to be "modern" here. Can someone help?

  • Maria Droujkova   24 januari 2012 16:36
    Reageer op:   Bon Crowder   24 januari 2012 10:41

    Bon, my hope from the two tasks this week is to crowdsource a good definition of "modern math" or "21st century math" (to be more particular). The first task is a scavenger hunt of sorts, and the second task is about design - unless people remake tasks to be something else. My plan is that we will know modern math when we see it, and from these examples and looking at their features, a definition will emerge.