How Do I Learn and Some Reflecting

How do I learn? That's a really big question. I guess I like to learn by doing and trying. Looking at an activity that's put in front of me and actually physically engaging in it. In our discussions at our table, we talked about some of the different ways we learn. Some of them are doing, seeing, acting it out, revisiting the task and reflecting on the process of what was just done. 

Does this mean our students learn the same way? Is it something we've taught them over the years or do all people learn in these ways? These are important questions I'm trying to figure out. 

The most effective way for me to learn is by making mistakes and reflecting on why I made that particular mistake. After reflecting, I can then go and fix what went wrong and work on not making the same mistake again. 

When we did the knot activity last time we were together, I don't think I did it the correct way by actually making the knot, I just made the design of the knot. In the end does it really matter because I know I learned that I need to make mistakes in order to learn. 

I try to be reflective after a days work with the students by asking myself; How did the lesson go? Did they understand what the point of the lesson was? What could I have done differently? Where do we go from here? What could I possibly do differently next time? And even many more questions. What I don't do a lot of the time is actually write down my reflections and keep track of the changes I need to make regarding my lessons. Maybe I need to do a better job of this especially with the changes I am wanting to make regarding my work with 21st Century Competencies and how I want to embed them into my lessons and investigations. The other area I am discovering I need work in is inquiry.

I think I understand it but when I visit other places like The Genesis Learning Centre in Edmonton, AB I realize I've got some work to do. At first I wasn't okay with this but you've got to take a step back and realize you can't make ALL the changes in your classroom in a short amount of time. Baby steps are important. Asking quality questions is also important. I worked on that this week and it was difficult for some of my students to come up with answers to those questions. One of them I used during writer's workshop was, Why do you think this is a good piece of writing? The student just looked at me blankly and thought and thought. At that time, I realized I needed to be asking them to really think in this way so I've got some work to do. 

It appears as though learning is an ongoing process which requires us to be reflective and thoughtful about what we ask and why we're asking the questions we do. Inquiry is an area I need to improve upon and work towards more critical thinking and asking quality questions of my students. I guess I better get to work. 

What Are We Doing To Kids?

Every Wednesday I tutor a former student I had 2 years ago in grade 2. He's now in grade 4 and I'm continuing to build upon the knowledge he learned from me as well as his grade three teacher and help him make sense of multiplication and division and all the other math ideas in the grade four curriculum. WELL, when I walk into the room and look on my table this is what I saw.

Are you getting ready for my rant? Here we go... I'd like to know why are teachers so focused in on giving kids worksheets at this time of the year or at any other time of the year. I'm not talking one worksheet to practice an idea or a skill but 6 pages in a booklet. 

Here's the scenario... I come in the room and see a page with 7 division questions along the top and 12 rows going down, yes you can do the math. That's 82 questions on ONE page, all division. Well that's just one page, there's another and then another with just half of the page covered with division questions. But wait, when I look further there are 3 more with various other questions, yes all division. The front page even looked like this:

 The theme of the page was Jersey Division. I'd like to know what Jerseys have to do with division? If anyone can tell me then please message me because I'm up for the discussion.

It takes us 1 hour to get through 70 questions. Remember there are 5 more pages to go but the good part is that he has until Monday to get the booklet complete. But wait, it takes one hour to get one page done and he's got 5 more to do. That means one hour each night until Sunday. WAIT...THERE'S MORE. He's got 2 other booklets to complete along with LA, Social and Science work. Remember it's June and we've got 4 weeks left of school. All of the kids are done and I mean DONE. The weather is nice and this particular boy, along with lots of other boys need to be out running around, playing, riding bikes and having fun. Not inside doing copious amounts of math worksheets and booklets.

The point of this story is why are we giving kids this amount of work? Why are we giving them this kind of math? Just so we can say we've "covered it!" Do kids really gain from this type of work? Are they really learning their multiplication and division facts by doing gobs and gobs of the same 'ol shit. Excuse my language but this makes me crazy.

After cooling off for the past couple of days and speaking to various people, I'm still frustrated by this. Why you ask? First, this amount of work is not appropriate for this time of the year. Second, this type of math isn't problem solving, thinking, critical thinking, reasoning, explaining, making connections, etc, etc. It's busy work to make it appear the curriculum has been taught. Thirdly, it's bad practice on the teachers part and it's bad leadership on administrations part. This teacher is doing this because there is support from administration to teach the drill and kill method. I've heard it several times from administration that kids need to know their basic facts and this is the way to do it. This teacher should be expected to teach the new curriculum and support should be provide. Clearly this is not the new curriculum and support is not being provided to this teacher.

There are a handful of us in our school who are working at changing our practice but it's frustrating when you work hard to get your students starting to think, problem solving, reason, make connection and talk about their learning then they move to classrooms where this takes place. What are we to do? I do not have an answer to this question but I do know that I'm not going to stop learning how to be a better teacher and helping my students make connections, problem solve, think and push them to do better and know more. It's shameful and I would be embarrassed if I was this teacher. Our students deserve more from us.

Continuing to Build

Building, building, building is the theme of the classroom. You'd have thought after building the number 25 for the past 5 days the kids would be really good at it and much faster. Well I'm here to tell you that's not the case. I did manage to snap a couple of very fast pictures of kids who stretched the area model out into the number line.

You'll see the paper model doesn't match with the manipulatives. Many are quite concerned by the length rather than the sequence of numbers should make sense.

 Both of these students are understanding that the two models need to match. What they were unclear of is how to move from 25 to 100 using this model.

I like how she's kept the green (25) altogether.

To see the relationship between 25, 75 and 100 I had the students build 75 today. We went right back to the same behaviours of not knowing what to do. I guess this tells me a couple of things.

1. We need to do WAY more building of number. 
2. We need to build more numbers and talk about them. 
3. I think we're going to build the 100 model using adding machine tape so that it is always available and easy to access. The blocks are really cumbersome and they don't take them apart properly. Or maybe I need to rethink this and continue to have them use the blocks because at some point they'll figure it out. 
4. I need to be more patient. Today was frustrating for them and me. We'll continue tomorrow and I know it will be better. 
5. The numbers need to stay on the tool. Part of the problem for them is not seeing that the 75 square on the paper (the last place they cut) is also the spot where the numeral 75 should go. That's if they start in the correct place. If they haven't put the numbers in the correct places, all kinds of weird and wacky things end up happening. The chunk of green doesn't end up staying together so then it becomes different. 

I just had a brain wave. What happens if I have them write the 5 number sequence or just the 10 sequence on their paper, then have them color in the number I'm wanting them to make. Will this make a difference? Will they see that the number they are embedding needs to match up with the numbers they've placed on their 10 by 10 grid? I'll let you know how this goes.

Connecting Area Models to Linear Models to 100

First let me start off with a big HELLO! It's been months since I've posted. The content of this blog will change from a technology component to that of a math focus. It was always my intent to use this blog as a space to open up the conversation about math thinking in a primary classroom, namely my own and that of the students, with a focus on grade 2 curriculum. It's a work in progress and I've got lots to share so please return frequently and I look forward to the conversations to come.

Our grade 2 curriculum in Alberta says, students need to represent and describe numbers to 100, concretely, pictorially, and symbolically. As a class we've been working on this all year but we're revisiting it again to help pull and develop math strategies.

One of the strategies AB Learning recommends is using addition o subtract. The goal in the images you'll see below is to help build the connections between the area model and move it into the linear model of a number line. My goal is to show how the two are connected as well as work on placement of numbers in the area model and linear model. 

Students built 25 and 100 and the task was to compare them to each other. Many students were very good at pulling the chunk of 75 from the 25 and then using strategies like making tens, transforming the chunk of 25 and doubling it, some counted 10, 20, 30,...to 70 and then added 5.

You'll see from the model, the students could easily count the tens and fives. This picture does not lend itself to easily seeing the adding on to get to 30 from 25 or adding a 10 to get to 35 but it's the model the student built and there were others who built it as two tens and the five ones. I just didn't get a picture :-).

From here we talked about the decade numbers (tens) and where they would go on the grid. Lots of good discussion was had around where it should go and why. In the end, students placed their numbers in various places on the grid. Some up in the left hand corner others bottom left. It depended on what they were thinking and where they placed their 25.

You'll see here that this student is building it backwards. It's not a concern of mine because they are understanding their own sequence. I must add that writing the numbers on the blank grid was a challenge for some of them. I didn't leave them hanging because they then stretched it out into a number line to see the connections between the numbers. Now this student I watched because of where the numbers were being placed on his rod.

This student is going to have difficulty taking the area model out into a number line because they are just writing out the pattern of numbers and placing all the stickers on the one rod. Many ran into this problem but eventually worked it out with help from another student or listening to what others were saying.

I didn't want all of the numbers written on the grid because it's not about seeing all the numbers it's about making connections to the relationships between the numbers and where they fall on the open number line. Remember, my goal is to make connections and eventually build the understanding of adding to subtract. Before I can get them to this strategy they need to understand several different ideas here.

1. Where are the numbers in relationship to each other on the area model and the linear model.
2. Comparing the two models and being able to use them the same way. 
3. It's possible to move from 25 to 100 or from 100 to 25 without moving the large chunk. HUGE IDEA!!!
4. The two models the same but just organized in a different way. 
5. The number 25 is embedded in the number 100. Another HUGE IDEA!!

After placing the numbers on their paper copy and their manipulative copy, the students took the area model apart and stretched it out. A lot of misunderstandings were somewhat cleared up and others realized they'd made some mistakes along the way. It's okay because we'll come back and build more and more of these models. Unfortunately, I didn't get pictures of the linear model but I will next week because all of them didn't build it.

There were some interesting connections being made once they moved to the linear model. Some said, "Ms. Brown, did you know there are 4 - 25's in the 100?" Great connections. "There are 5 - 5's in 25?" Others were asking, "Why didn't the paper model match with the unifix model?" They kept trying to place the numbers side by side on both models but the paper model was longer. Sorry, no explanation for that one other than the paper was actually a bit bigger and wider than the blocks. Hopefully, I can get a picture of that next day.

When they built both models I wanted them to compare the two. I think it's also important to realize that students don't always have to put the 1 in the same place. You'll see various images where the 1 is opposite. It's all about their understanding and how they build it. It's our job to take their thinking and help them make sense of it. Not to put them into our way of doing it.

Have they finished making connections and do they know everything they should? Absolutely not!!! We've only just begun. More building and discussion needs to take place. We haven't even gotten to the idea of using addition to subtract but I know someone will lead us into this strategy without me having to tell them. 

Mrs. Claus Pattern Problem

Mrs. Claus Pattern Problem 1, a set on Flickr. If you are working on patterning and problem solving, this is a great problem to try with your students.

This blog will now be used as a way to share my students math thinking and that of my own. I hope you enjoy the new format. I would love to keep a discussion going about student work. Please feel free to try the problem with your students. I would love to hear what yours did.

Here are some photos of how my students (Grade 2's) solved the Mrs. Claus problem.

Mrs. Claus is decorating cookies for the Elves Christmas Dinner.

She lined up the first 20 cookies and put icing on every second one.
She put a cherry on every third one.
How many cookies will have nothing on them? Show how you know.

Do some cookies have icing and a cherry? How many?
Do you see any patterns?

You write a similar problem......
The students were allowed to use any materials they wanted, paper, white boards, manipulatives, combination of any of these. The first part of the problem took us a class block. I had numbered the photos 1, 2, 3 to show you the order they were taken in as well as the progression of their thinking.

As you can see from many of the photos they were stuck on the idea of thirds. They grouped the cookies into three's giving the middle cookie the place of second each time and the last cookie the third placement with the cherry going on top.

After looking through the pictures and evaluating our discussion today, they did the problem this way to over compensate for not understanding that a cookie could have icing and a cherry on top. Many of them wanted to have a space after the cookie with the cherry on top.

Further Flickr Findings

I would like to return to the tool of Flickr and discuss some of the things I have learned in the past couple of weeks about this social photo-sharing website. Flickr has the ability to impact education in many ways but I feel it has fallen short in others.

History
I had heard about Flickr from people on Twitter and family members who have sent me invitations to view photos of my nieces and nephews. I hadn't really given it much thought for education until this project. I had remembered our professors saying the images from Google were not always the best to be using for research, Flickr was a better site for being able to reference and give credit where it was due. Upon further investigation into Flickr I because interested in it's popularity among educators and how they use it in the classroom. I also wanted to know more about the tagging and RSS feeds. How did they work and why are tagging and RSS feeds important.

What do I really like about Flickr?
1. Flickr allows you to share photos with Blogger, Twitter, Tumblr, and Wordpress right from the actual Flickr site. I tried this feature this week and I quite enjoyed the ability to quickly upload and write about my photos at that moment without having to do extra steps.

2. When you subscribe to a groups photostream RSS feed, it is sent to your aggregator of choice, mine happens to be Google Reader. This is a feature I really like. Having the photos comes to you is much easier and helps to keep you updated. You could then share them to Twitter or make comments on your friends images or tag the picture with a note.

3. Flick has thousands of photos uploaded each day, which makes the possibilities endless for finding a photo. There are so many to choose form. The 'explore galleries' tab was really amazing. There are some amazing amateur and professional photographers around, it a great time waster during crunch time for sure.

4. Discovering the Flickr Uploader on iPhoto makes adding photos so much easier than how I was doing it before. It will be much easier to now upload photos to my photostream, Blogger, Twitter, and my groups using this feature in iPhoto. You can read my blog post about the Uploader feature here.

5. Flickr offers a widget photo stream for your blog. I added one to my classroom blog and one to this site. It shows the most recent photos added to Flickr. If I or my students need to quickly access a photo I can click on it and it sends you to the most recent set I uploaded. I use it a lot in math to discuss student work in the classroom. You could also add images from Flickr and have each student click on an image of choice and then write about about what they see, it would depend on the task and what you wanted them to think about and reflect upon.


What I was bothered by in Flickr
1. If you click on one of the photos from my photostream on this blog,  I thought people could make a comment on the photo. I was incorrect, only contacts can make comments and you must be signed in to do so. For example, I was going to have students explain their thinking about the pattern they saw in their own work. When they clicked on the photo, it opens up to the site and it appears you can comment but it takes you to the sign in screen. This is a definite con especially if I am wanting others to make comments. I will need to create a class Flickr account, share the log in name and password with students and have them sign in. This video provided some excellent ideas on how to use further use Flickr in the classroom.

2. Flickr does not offer an educational feature like Diigo does. Perhaps having a safe place where teachers could upload photos and students could search this data base of images is something Flickr will think of for the future.  But for now, Standen says, the group feature is a way to go around possible problems with the search feature and kids coming across unnecessary photos.

much of what's not kid friendly about Flickr can be eliminated by skipping (or greatly limiting) use of the Search button. One way to do that is with Flickr's Group tool. Flickr's groups are small pools of users who pull photos from across the site and organize them into categories accessible by group members

This would mean, creating a group and posting the link on a wiki or blog where students had access to it.

3. Due to the huge number of uploads each day, Flickr has the potential to be an unsafe site for students. Who is controlling all of those uploads? This photo shows how many photos are uploaded in a minute.

This is an amazing number in one minute. In 2008, Educause reported over two billion images to be on Flickr,  the amount of images present three years later is astronomical. The report goes onto state: 

Flickr largely depends on the community to police itself for copyright violations, and opportunities for libel or invasions of privacy around.

This can be a frightening thought for a teacher who does not want to take the risk of students finding an inappropriate photo.

4. Searching for photos can become daunting. I found searching to be quite difficult. It could be that I am not using the correct words or tags but I often feel I cannot find what I am looking for. If I find it difficult, kids could potentially experience the same problems. A teacher may need to search photos ahead of time and upload them to a group site, students could then search through the site. It seems like a lot of work. It would depend on how many photos one was looking for and the tags and subject of the photo being used.

5. I couldn't find a group that I really wanted to join, so I created my own. You can take a look here. I am hoping to have conversations about student work in math. If I keep adding to the group and posting updates to Twitter I am hoping to engage in some great discussions about student thinking. I think these group discussions will be a way to collaborate with others using authentic photos and actual student work. This is something I feel is missing in math instruction. In order to really reflect, we need something to reflect on. Sullivan (2000) stated it nicely when she said this:

I still have ideas that I think are uniquely my own, at least in part. But I know that a lot of other people are thinking about the same thing as I am, just perhaps in a slightly different way, through a different lens.

What a better opportunity to invite other educators into the conversation around mathematical thinking than reflecting and sharing their ideas on their students work.

Overall, I think Flickr is a useful tool to use in a classroom and for personal use. It took some time to learn about all of the many features and I still do not feel completely confident in knowing all of the ins and outs of Flickr. However, I would recommend exploring and using this Web 2.0 tool in your classrooms. I look forward to keeping you posted on how my Flickr group is going.

References

Educause. (2008). 7 Things you should know about flickr. [PDF]. Retrieved from http://www.educause.edu/ELI7Things

Johnson, C. (2010). What does it mean to “reflect on my learning?” Critical Thinking at Forest Green School/CFL. [Blog post].Retrieved from http://ct.forestgreenschool.ca/2010/11/15/what-does-it-mean-to-reflect-on-my-learning/

Jutecht. (Producer). (2006). Flickr. [YouTube Video]. Retrieved from http://youtu.be/QLo4355l6QE

Standen, A. (2007). My friend flickr: a great photo opportunity. Edutopia. http://www.edutopia.org/flickr-social-networks-sharing-photographs

Sullivan, K (2000). What does reflection mean to us? From Now On The Educational Technology Journal. [Blog post]. Retrieved from http://www.fno.org/apr2000/reflection.html

The Power of Tagging

I am so excited!!! I know this doesn't have anything to do with reflecting on my actual blog but I was pretty pumped about what I saw. I wanted to show the power of tagging. I showed it to my students this week and never got around to doing anything more with it. Tonight, when I looked on our classroom blog I had a student who was trying out the idea. You can see that she has tagged her post quite accordingly. We're also working on adding voice to our writing and you can see she is well on her way to getting it. Sometimes you just need to put the idea out there and see what they come up with. If you wanted to comment on the blogs, just click on the picture.

Hope you enjoy this little tidbit of information