Math + Manipulatives = Happy Students

I’m old, therefore, I can’t remember back 30 some odd years ago to when I had a good math lesson in elementary school. But, I spent a few days observing math lessons at the kindergarten where I work earlier this month, and I loved what I saw. Ms. Fox had lessons that were engaging and full of manipulatives for the students, and I loved her style of classroom management. In a class of 20, she has them broken down into 4 groups of four to five. She sets up the 4 tables in the classroom with different math activities, and the students rotate around the room. I want to steal her management style for telling students when it’s time to rotate; she says, “Macaroni and cheese,” and they respond, “Everybody freeze.”

Filling in the number of dots based on the number below

At the different tables, there were worksheets along with a variety of manipulatives. One table had a 10-frame page with dots in each frame and unifix cubes. Students were told to count the dots on their worksheets and then build a tower out of the cubes with that number of dots. It was cool to see how tall some of the towers got. There was another table that had cups of beans. They were instructed to flip them and count how many beans landed on the blue side; once they knew that number, they had to color in that number of beans on their worksheet.


Coloring the number of blue beans that flipped out of their cups

On the first day I was there, Ms. Fox told me about the Starboard in her room. She said, “It’s really cool, when it works.” On the third day, I got to see a major Starboard fail. She had a digital spinner ready to go, but the Starboard wouldn’t work. So, thinking on her feet, she made a spinner in class with a piece of cardboard, a pushpin, and a paper clip. I was impressed with how quickly she transitioned into a new plan and how she kept student interest with the use of creative problem solving. When the paper clip would land on a number, she would ask students what number was before or after the number they had landed on. The students couldn’t wait for their turns!

The impromtu spinner that was made in class



Abstract Mathematics

When I was first taking Child Development classes 5 years ago, Piaget rocked my world. I felt like his stages of development were spot on, and his theory resonated at my core. Sometimes, when I am reading a story to my preschoolers, and I ask if they’ve understood what I’ve just read, I realize that it was asking them to think abstractly. Since I’m dealing with 3 and 4-year-old students, they just stare at me with blank looks on their faces. Because they are in the preoperational stage of thinking, they need stories to spell things out clearly.

Eight is Enough_Ken_Flickr

Eight is Enough” by Ken is licensed under CC BY 2.0

There is an amazing quote from Piaget that speaks about the issue of only teaching in the abstract.

“Abstraction is only a sort of trickery and deflection of the mind if it doesn’t constitute the crowning stage of a series of previously concrete actions. The real cause of failure in formal education is therefore essentially the fact that one begins with language instead of beginning with real and material action.” – Jean Piaget, 1976

For me, this lays out the fundamental problem with teaching children in abstract ways, rather than building up to abstract concepts with concrete demonstrations. Students need to be hands on and manipulating materials, in order to understand the process of things.

Jean Piaget_Anton Johansson_Flickr

Jean Piaget” by Anton Johansson is licensed under CC BY 2.0

Many decades ago, when I was in elementary school, the main way I was taught subject matter was in an abstract fashion. We never had manipulatives or something concrete that could represent what we were learning. Instead, we were given rules, formulas, and definitions, and we were told we had to memorize them to succeed. It was very difficult to learn that way, because there wasn’t a deeper understanding of the why. I can remember numerous times when I was younger having the light bulb turn on in my brain, because I’d suddenly figured out why I’d been doing something a certain way my whole life. Instead of just memorizing the multiplication tables (abstract), why not show how multiplication is just a faster form of addition with something like beans or marbles (concrete)?

multiplication table_Denis Mihailov_Flickr

multiplication table” by Denis Mihailov is licensed under CC BY 2.0

Math: You Can Do It!

Back in the day, some 35 years ago, I knew I wasn’t good at math. It’s just the way things were. I’m not sure who instilled that idea, whether it was teachers or fellow students. I know it wasn’t my parents, because they were always trying to bolster my self-esteem, not undermine it. Growing up, I was good at English type things: vocabulary, spelling, writing; and that was good enough for me. How sad! I just gave up on applying myself at a very early age.

home work routine woodleywonderworks Flickr

home work routine” by woodleywonderworks is licensed under CC BY 2.0

It wasn’t until I got to the junior college level and needed math courses that I discovered I was actually able to learn and do math. I didn’t want to just submit my high school transcripts and go straight to Algebra; I knew I needed to start from the beginning, since it had been 20 plus years. So, that’s what I did. I sat in the math lab at Oxnard College for hours working on module after module. To my amazement, I was not only passing, but I was doing well. I was excited. Imagine that, a forty-year-old realizing she’d told herself the wrong story about her abilities in math her whole life. What else might I have been wrong about?

Math Workshop Portland 7 US Department of Education Flickr

Math Workshop Portland 7” by US Department of Education is licensed under CC BY 2.0

I kept working my hardest through all my math classes and ended with College Algebra actually feeling like I was good at math. It was amazing, and it was sad that it took so many years for me to realize that. This late in life experience completely changed my view on who can be good at math; I think it’s anyone who applies him or herself. I understand that people will struggle, but I can’t help but wonder how many people have mental roadblocks that were created at an early age that were never eradicated. As a teacher, that is what I aim to do. I want to eradicate the negative biases that children have of themselves and encourage bravery and risk taking to help them be successful now and not when they are middle-aged.

Pi number J. Gabas Esteban Flickr

Pi number” by J. Gabas Esteban is licensed under CC BY 2.0

Technology Whirlwind

Over the last 10 weeks, I’ve been exposed to various new forms of technology through the college course titled Learning Technology for Educators. Now, we’re at the end of the semester, and it is time to start visualizing how I can use all the technological tools I’ve learned in my own classroom. Looking back, we really did accomplish a lot: from blogging, to social media, screencasting, Flipboard, animated movies, and the big one, a Webquest.

IMG76” by US Department of Education is licensed under CC BY 2.0

It probably comes as no surprise, since I’m a part-time radio DJ, that my favorite tool and one I’ll be using a lot in the future is screencasting. This semester I became very familiar with Snagit. I really enjoy being able to easily show someone how to do something right on my computer screen. I can see how valuable this tool will be as a teacher. I’ll be able to create lessons with a screencast or answer a student question about how to navigate a website or issue.

Copyright Commerical

I enjoyed learning how to use the tool PowToon to create my copyright commercial. I’m sure there are many animators who don’t like how simple PowToon makes it for the average person to create a movie, but that seems to be the trend of everything in technology: make it simpler and easier for everyone. Speaking of simple, who knew creating your own website was so easy? Not me! But, Google Sites has created an easy layout so that anyone can create their own website. You can choose a template or go the hard road and create your own layout like I did. I used Google Sites for my Webquest From the Ground Up. After spending countless hours on the site, I think I’ve finally got it down after a lot of trial and error. But, isn’t that what all technology boils down to? You keep trying different things until you find something that works.

Screencast of the Webquest “From the Ground Up”

After the last 10 weeks, I have a new appreciation for the art of blogging. I never wanted a blog before, but now that I have one, I keep having ideas for future blog posts. “Can you fall in love over text message?”, “Life without a uterus”, and “Parents, please stop wiping your child’s bottom” are a few that keep running through my head. I like how much critical thought is put into blogging, and I can see that it’s an extremely valuable tool for students to cultivate. Another valuable tool someone learns when he or she becomes a blogger is how to use Creative Commons images and media. I became very familiar with Flickr and the proper way to site an image. This is vital in today’s society where students sometimes think that anything on the internet is free. Images on the internet are not free, and you should always give credit for the material you use.

Always Ask Permission

Copyright symbol” by David Wees is licensed under CC BY 2.0

This week at school, we dove into the confusing and word-filled world of Copyright law. To say it is impossible to keep all the rules in mind is an understatement. I am feeling overwhelmed, and I already had a decent understanding of copyright law. Working as a radio DJ and video editor in the past, there were always pieces of music or images that we couldn’t use. One time, the company I edited videos for was sued by the family of Einstein for using his image without permission. That “mistake” cost them $10,000, and made me extremely aware that using copyrighted material can have grave consequences.

Copyright” by Saad Akhtar is licensed under CC BY 2.0

Teachers must be knowledgeable of Copyright law and respect it, otherwise their school district could be found liable. The Fair Use doctrine allows teachers some leeway, but it really only provides a limited basis for using a copyrighted work. Most teachers are aware of the Copyright Act which allows educators to copy some items, but again there are limitations. Examples of what can be copied are a poem of 250 words or less, or up to 250 words of a longer poem, a single chapter from a book, and an article, short story or essay of 2,500 words or less. See what I meant earlier? The rules involved with Copyright law are overwhelming.

copyright takedown notice” by Andrew Allingham is licensed under CC BY 2.0

Copyright law is more important than ever for teachers to understand and help students understand. Growing up in the digital age, students think that anything on the internet is free for the taking. But, it is crucial for them to understand that the internet is not the public domain. Things in the public domain are typically very old and nothing created since computers came into existence is even close to entering the public domain. Teachers and students must become comfortable with requesting permission to use images, music, stories, articles, and basically anything created by someone else. And, they need to be familiar with how to use things that are Creative Commons. When someone has put the CC license on their work, it means the owner is making the work available to others while reserving some rights to it. A great place to look for Creative Commons material is on Flickr or Wikimedia. To sum up this very complex issue, assume a work is copyrighted and ask permission to use it.

A Love/Hate Relationship with Social Media

Myspace 선물” by egg (Hong, Yun Seon) is licensed under CC BY 2.0

Back in the day, there was myspace. I say that because about 9 years ago I decided to completely ditch myspace for Facebook. At the time, it seemed like myspace was a dying site, and Facebook was taking over the world. Today, it seems like that assessment was mostly correct. The thing that still draws me to Facebook is the fact that I’ve been able to keep in touch with distant family and reconnect with friends from decades past. When Instagram came around, I was drawn to the idea of having a site for just posting pictures, so I joined it as well.

Twitter” by Kooroshication is licensed under CC BY 2.0

For many years, I have been happy maintaining just those two sites. And, I say maintaining because for me, it is a chore. I don’t like putting all of my personal business online for the world to see, and I feel a little creepy spying on people I used to know 20 or 30 years ago. I’ve had many people try to get me to join Twitter over the years, and I flat out refused. Then, one night in my technology class for University of La Verne, I was forced to join. I can see the appeal of Twitter, but it also seems like a site that is losing steam. I have a lot of friends in the radio business and most of them aren’t using Twitter anymore. It seems most have migrated to sites like Snapchat (another one I have refused to join).

Edmodo screenshot by Jennifer Conter

It seems that all future teachers are being told they will be using Twitter in the classroom. I can understand the appeal of having students put their own words on display for the world so they can get accustomed to a true response. It can be hard taking criticism and what better place to build up a thick skin than in the realm of social media? The fact that this blog is available for anyone to read makes me much more conscious of the words I type, and the same thing happens with our students. I’m not sure I will be using Twitter in the classroom, but I definitely look forward to using a site like Edmodo. I really like the idea of a safe online environment that is just for students, teachers, and parents. Edmodo has also made the very intelligent move to incorporate Google Apps for Education and Microsoft Office into the site, so I can’t wait to dive into it.

Ready, Set, Periscope

I recently had an assignment for school where I had to find an edtech tool that I thought would become popular in classrooms. After reviewing hundreds of tools, I decided to go with one that took me a bit out of my comfort zone: Periscope. As a former video editor for an organization in Los Angeles, I am no stranger to the concept of streaming. Even with that being the case, I’ve never had the desire to broadcast myself around the globe. But, after doing some research, I see a whole new world of possibilities with the app, Periscope.

Periscope logo

Periscope is an app you can put on your iOS or Android device and use to stream anything you want to the world or just a select group of people. Periscope was acquired by Twitter before it launched in 2015, so you can easily create a login with just your Twitter account. Since many classrooms today have already incorporated tweeting into their lesson plans, I think the next logical step will be live streaming. I see Periscope being used to broadcast important classroom moments, graduations, and even for use with homework.

Red dots are live broadcasts happening in real-time on Periscope.

As with anything, there are some pitfalls to using this kind of technology. First, it requires users to have a cellphone and one with plenty of data in the event that they want to stream something but are away from a Wi-Fi signal; the last thing teachers need is an angry mob of parents yelling about data charges. The second pitfall that causes concern is that this will be a very difficult tool for shy and reserved students to use. My hope is that by using this type of technology, it could help them come out of their shells and maybe even find a voice they didn’t know they had.

With Periscope, viewers can interact with broadcasters in real-time.

At the moment, Periscope has a lot of competition because everyone wants to get in the streaming game. Meerkat was Periscope’s main rival, since both apps launched at the same time in 2015. But, just last week Meerkat shut down, so they are no longer part of the equation. Facebook recently jumped into streaming by launching Facebook Live and got a great deal of attention by having celebrities use it. There are also sites/apps like YouTube Live, Snapchat, and Livestream that offer streaming, just to name a few. I think that since it has Twitter as its main support system, Periscope stands the chance of being around for many years to come.